Answer:
a.) X ≈ N (0, 12)
b.) Y ≈ exp(2)
c.) The given distribution is not defined.
d.) Not a standard form of any distribution .
Step-by-step explanation:
Given - In parts (a)−(d) below, either use the information given to determine
the distribution of the random variable, or show that the information
given is not sufficient by describing at least two different random
variables that satisfy the given condition.
To find - (a) X is a random variable such that Mₓ(t) = [tex]e^{6t^{2} }[/tex] when |t| < 2.
(b) Y is a random variable such that [tex]M_{Y}[/tex](t) = [tex]\frac{2}{2 - t}[/tex] for t < 0.5.
(c) Z is a random variable such that [tex]M_{Z}[/tex](t) = ∞ for t ≥ 5.
(d) W is a random variable such that [tex]M_{W}[/tex](2) = 2
Proof -
a.)
As we know that the moment generating function of normal distribution is given by
Mₓ(t) = [tex]e^{ut + \frac{1}{2}t^{2} \sigma^{2}}[/tex]
Now,
Mₓ(t) = [tex]e^{6t^{2} }[/tex]
= [tex]e^{0(t) + \frac{12}{2} t^{2} }[/tex]
⇒μ = 0, σ = 12
Nd it is represented by
X ≈ N (0, 12)
b.)
Moment generating function of exponential function is given by
[tex]M_{Y}[/tex](t) = [tex]( 1 - \frac{t}{\theta})^{-1}[/tex]
Now,
[tex]M_{Y}[/tex](t) = [tex]\frac{2}{2 - t}[/tex] for t < 0.5.
= [tex]\frac{1}{\frac{2 - t}{2} }[/tex]
= [tex]\frac{1}{1 - \frac{t}{2} }[/tex]
= [tex]( 1 - \frac{t}{2} )^{-1}[/tex]
And it is represented by
Y ≈ exp(2)
c.)
Z is a random variable such that [tex]M_{Z}[/tex](t) = ∞ for t ≥ 5.
The given distribution is undefined.
d.)
[tex]M_{W}[/tex](2) = E([tex]e^{2w}[/tex] )
= [tex]\int\limits^{-\infty}_{\infty} {e^{2w} f(w) } \, dw[/tex]
= 2
It is not the standard form of any distribution.
Factorise 9x^2y+12xy^2
Answer:
3x(3xy + 4y^²).
Step-by-step explanation:
Mskqkkqkaak
1. You want to put new carpet in your bedroom and the dimensions of your room
are 8.74 ft and 10.3 ft. If you want to find the area of your room to put new carpet
in, which of these problems would help you estimate how much carpet will you
need to buy?
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that a new carpet is to be put in the bedroom and that the dimensions of the room are 8.74 ft and 10.3 ft.
The area of the room will be the multiplication of the dimensions given. This will be:
= 8.74 × 10.3
= 90.022
= 90ft²
What is answer for (11x-32)=45
Answer: x=7
Step-by-step explanation:
A school raised $18,000 at a charity event. A, B, and C, in ratio 1: 2: 3. How much money did each charity receive?
Answer:
3000
6000
9000
Step-by-step explanation:
18000/6=3
A=1(3000)=3000
B=2(3000)=6000
C=3(3000)=9000
Evaluate the logarithm log 0.001
Answer:
Make sure to click on the png file the steps and answer are there!
The function d =
45t gives the distance d Juan traveled in miles after t hours.
is this discrete or continuous data?
Answer:
Continuous data
Step-by-step explanation:
Given
[tex]d = 45t[/tex]
Required
Discrete or Continuous?
From the question, we understand that t represents time in hours. This is a continuous data.
When multiplied by 45 to give distance, the resulting data is also continuous.
Hence, [tex]d = 45t[/tex] is continuous
Answer:
d = 2.5t, continuous
Step-by-step explanation:
Just did it on Edge and got it right
A full-time employee who works 40 hours per week earns $27.50 per hour. Estimate that person's income. Round 52 weeks to 50 weeks per year, and round the hourly wage to the nearest dollar for the estimate. what is the estimated of annual income?
fifty five thousand 55,000
Find the surface area of this rectangular prism: Don't forget to show the unit of measure.
Answer:
jejdujehehtjejehevgshfjrjehrhdb
Step-by-step explanation:
jsjdrbhrry4hebzbs d rhyeush r dbru4hu4 dbb
Please help me
What type of association does the graph show between x and y?
Answer:
Linear positive association
The measure of angle A in ABC is twice the measure of angle B and the measure of angle C is 20° less than the measure
of angle B. What are the measures of the angles in ABC?
Answer:
m∡A = 100°
m∡B = 50°
m∡C = 30°
Step-by-step explanation:
let 'x' = m∡B; 50°
let '2x' = m∡A; 100°
let 'x-20' = m∡C; 30°
x + 2x + x - 20 = 180
4x - 20 = 180
4x = 200
x = 50
B. Subtract the following integers
16.9 - (-5) =
17. - 12 - ( + 8) =
18. 15 - 9=
19. - 5 - (-8)=
20. - 11 - ( + 14 ) =
Answer:
16. 9 - (-5) = 21.9
17. -12 - ( + 8) = -4
18. 15 - 9 = 6
19. -5 - (-8)= 3
20. -11 - ( + 14 ) = -25
Step-by-step explanation:
Subtracting a negative from another number is the same as adding the number. Thus, 16.9 - (-5) = 16.9 + 5.
Hope it helps <3 :)
Answer:
16.9-(-5)=21.9
17.-12-(+8)= -3
18.15-9=9.15
19.-5-(-8)=22
20.-11-(+14)=-5
Help please with this
Look at picture
Complementary angles
Answer:
70°
Step-by-step explanation:
80° - x + 80° = 90° { being complementary angles }
160° - x = 90°
x = 180° - 90°
x = 70°
Hope it will help :)
3. FIELD TRIP There is space for 120
students to go on a field trip. Currently
,
74 students have signed up. Write and
solve an inequality to find how many
more students can sign up for the
field trip.
i need help plz
well if
120-74=46
then 46 is the correct answer.
74+46= 120
46 more students can sign up for the field trip.
Answer:
74 + (x) = 120
Step-by-step explanation:
subtract 74 from 120
120 - 74 = 46
I have a quick question please someone answer Is 5/8 irrational?
Answer:
no
Step-by-step explanation:
5/8=0.6250 so its rational
Answer: no
Step-by-step explanation: 5/8 is rational because it is another way of writing the ratio 5:8. So no, 5/8 is not an irrational number.
the coefficient of x in the expression of(x+3) (x-1) is
Answer:
i think 4
Step-by-step explanation:
[tex]x^{2} +4x-3[/tex]
Please help ASAP if you know how. Thanks so much
Answer:
B) -6.61, 0.61
Step-by-step explanation:
Answer obtained by graphing the formula.
18 more than the product of k and 5 Evaluate the expression for the value of the variable, k : 7 Please type your answer in the box below. NUMBERS ONLY!
Answer:
The Answer Is 125.
Step-by-step explanation:
As, 18 More Than K Means
18 More Than 7
So, It's 25
Then Evaluate 25 With 5
It's 25(5)
Or 25 × 5
It's 125.
The difference between 30 and a number is 4.
Answer:
26
Step-by-step explanation:
30-4=26
thirty minus four equal 26
Write the equations of each line in slope-intercept form.
hi can you please help me with my work
Answer:
The answer is 3 1/2 inches!
Step-by-step explanation:
The average ratio of cats to dogs in the uk is 13:15 there are 5200 cats in the city of Bristol . Using the national average ratio , estimate how many dogs there are in the city of Bristol
Answer:
5,999
Step-by-step explanation:
A person who is standing on a ledge throws a rock into the air. The rock reaches a maximum height of 676 feet
above the ground after 1.5 seconds.
If the rock hits the ground below the ledge 8 seconds after it is thrown, which quadratic function can be used to find
the height of the rock above the ground t seconds after it is thrown?
Answer:
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta= b^{2} - 4ac[/tex]
Quadratic equation:
[tex]ax^2 + bx + c = 0[/tex]
The rock reaches a maximum height of 676 feet above the ground after 1.5 seconds.
This means that:
[tex]-\frac{b}{2a} = 1.5[/tex]
[tex]y_{v} = -\frac{b^2-4ac}{4a} = 676[/tex]
If the rock hits the ground below the ledge 8 seconds after it is thrown
This means that:
[tex]64a + 8b + c = 0[/tex]
Relation of b and a:
[tex]-\frac{b}{2a} = 1.5[/tex]
This means that:
[tex]b = -3a[/tex]
Relationship of c and a:
[tex]64a + 8b + c = 0[/tex]
[tex]64a - 24a + c = 0[/tex]
[tex]c = -40a[/tex]
Finding a:
[tex]y_{v} = -\frac{(-3a)^2-4a(-40a)}{4a} = 676[/tex]
[tex]9a^2+160a = -2704a[/tex]
[tex]9a^2 + 2864a = 0[/tex]
[tex]a(9a + 2864) = 0[/tex]
Since it is a quadratic equation, a cannot be 0.
[tex]9a + 2864 = 0[/tex]
[tex]9a = -2864[/tex]
[tex]a = -\frac{2864}{9}[/tex]
[tex]a = -318.22[/tex]
Finding b and c:
[tex]b = -3a = -3(-318.22) = 954.67[/tex]
[tex]c = -40a = -40(-318.22) = 12728.89[/tex]
The quadratic equation is given by:
[tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
hurry please ... LOOOOOLLL
Answer:
12 pounds of grapes cost $18.00
Step-by-step explanation:
The point, (12, 18) as plotted on the graph indicates that 12 pounds of grapes costs $18.
From the graph, we see that when x (pounds) = 12, y (cost) = 18.00.
Please please please answer this and show the steps. I’ll give Branliest to whoever replies first
Answer:
x = -3
y = 4
Step-by-step explanation:
distribute first
7x + 35 = 2y + 6
combine 'like terms'
7x - 2y = -29
do same steps for second equation
4x + 4y = 13 + 3x
x + 4y = 13
System of Equations:
7x - 2y = -29
x + 4y = 13
Multiply the first equation by 2 to eliminate the 'y-term'
14x - 4y = -58 (Now add this to the second equation)
+ x + 4y = 13
15x = -45
x = -3
Substitute -3 for 'x' to find 'y'
-3 + 4y = 13
4y = 16
y = 4
4k+1/2-2
Can Anyone help me
Answer:
4k-2/3
Step-by-step explanation:
Anybody know how to do lowest terms and can teach me how to get the answer to lowest terms questions?
Answer:
Step-by-step explanation:
6/9+x=7/10
x=7/10-6/9
when adding fractions both denominators must be equal, we’ll make them 90
x=(7/10)(9/9)-(6/9)(10/10)
x=63/90-60/90
x=3/90, the greatest divisor of 3 and 90 is 3 so divide both the numerator and denominator by 3
x=(3/3)/(90/3)
x=1/30
Centerpieces are normally distributed with mean of 30 ounces and standard deviation of 2 ounces. The weights of the shipping boxes are normally distributed with mean of 12 ounces and standard deviation of 1 ounce. Suppose that centerpieces are chosen at random and packed into randomly chosen shipping boxes.If a package exceeds 45 ounces, an additional charge is incurred. What is the proportion of packages will incur such a charge
Answer:
0.0901 = 9.01% of packages will incur such a charge
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Sum of normal variables:
When we add normal variables, the mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances.
Centerpieces are normally distributed with mean of 30 ounces and standard deviation of 2 ounces.
This means that [tex]\mu_C = 30, \sigma_C = 2[/tex]
The weights of the shipping boxes are normally distributed with mean of 12 ounces and standard deviation of 1 ounce.
This means that [tex]\mu_S = 12, \sigma_S = 1[/tex]
Suppose that centerpieces are chosen at random and packed into randomly chosen shipping boxes.
The shipment is given by the centerpice plus the shipping box. So the mean and the standard deviation of the weight are given by:
[tex]\mu = \mu_C + \mu_S = 30 + 12 = 42[/tex]
[tex]\sigma = \sqrt{\sigma_C^2 + \sigma_S^2} = \sqrt{2^2 + 1^2} = \sqrt{5} = 2.236[/tex]
If a package exceeds 45 ounces, an additional charge is incurred. What is the proportion of packages will incur such a charge
This proportion is 1 subtracted by the pvalue of Z when X = 45. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 42}{2.236}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a pvalue of 0.9099
1 - 0.9099 = 0.0901
0.0901 = 9.01% of packages will incur such a charge
The price on the price sheet of a new car contains the bottom line what is another name for this cost?
Answer:
C. MSRP
Step-by-step explanation:
Commonly called the sticker price because it’s the bottom line figure in a cars window sticker, is the base price plus any options
There are different kinds of terms. Another name that can be used for the cost above is Sticker Price.
What is the sticker price?The sticker price is also known or called the total MSRP. It is often said to be sticker price due to the fact that it is the conclusive ( bottom line ) figure found on a car's window sticker.
Tis also known as the base price with the addition of any other options, option-package discounts, etc. A person can purchase a vehicle for less than the amount of the sticker price.
Learn more about Sticker Price from
https://brainly.com/question/11947230
What is 7 1/5 written as a percent
Answer:
720%
Step-by-step explanation:
Answer:
720 %
Step-by-step explanation:
Method 1
If 1 is equal to 100 percent, then 7 would be 700 percent. 1/5 is equal to 20 percent. If you add 700 % and 20 % you will get 720 %
Method 2
7 1/5 is equal to
7/1 × 5/5 + 1/ 5 = 35/5 + 1/5 = 36/5
We know that 36/5 is the same as 36 ÷ 5
36 divided by 5 gives us 7.2
Convert the decimal to a percent:
7.2 × 100 = 720%
Hope this helps :)
PS. PLZZZZZZZ GIVE ME BRAINLIEST!!!!
what is 067÷ 32.16?
Answer:
2.08
Step-by-step explanation:
Answer:
2.0833333333333
Step-by-step explanation:
use calculator