The question is incomplete. The complete question is :
Let X be a random variable with probability mass function
P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6
(a) Find a function g such that E[g(X)]=1/3 ln(2) + 1/6 ln(5). You answer should give at least the values g(k) for all possible values of k of X, but you can also specify g on a larger set if possible.
(b) Let t be some real number. Find a function g such that E[g(X)] =1/2 e^t + 2/3 e^(2t) + 5/6 e^(5t)
Solution :
Given :
[tex]$P(X=1)=\frac{1}{2}, P(X=2)=\frac{1}{3}, P(X=5)=\frac{1}{6}$[/tex]
a). We know :
[tex]$E[g(x)] = \sum g(x)p(x)$[/tex]
So, [tex]$g(1).P(X=1) + g(2).P(X=2)+g(5).P(X=5) = \frac{1}{3} \ln (2) + \frac{1}{6} \ln(5)$[/tex]
[tex]$g(1).\frac{1}{2} + g(2).\frac{1}{3}+g(5).\frac{1}{6} = \frac{1}{3} \ln (2) + \frac{1}{6} \ln (5)$[/tex]
Therefore comparing both the sides,
[tex]$g(2) = \ln (2), g(5) = \ln(5), g(1) = 0 = \ln(1)$[/tex]
[tex]$g(X) = \ln(x)$[/tex]
Also, [tex]$g(1) =\ln(1)=0, g(2)= \ln(2) = 0.6931, g(5) = \ln(5) = 1.6094$[/tex]
b).
We known that [tex]$E[g(x)] = \sum g(x)p(x)$[/tex]
∴ [tex]$g(1).P(X=1) +g(2).P(X=2)+g(5).P(X=5) = \frac{1}{2}e^t+ \frac{2}{3}e^{2t}+ \frac{5}{6}e^{5t}$[/tex]
[tex]$g(1).\frac{1}{2} +g(2).\frac{1}{3}+g(5).\frac{1}{6 }= \frac{1}{2}e^t+ \frac{2}{3}e^{2t}+ \frac{5}{6}e^{5t}$$[/tex]
Therefore on comparing, we get
[tex]$g(1)=e^t, g(2)=2e^{2t}, g(5)=5e^{5t}$[/tex]
∴ [tex]$g(X) = xe^{tx}$[/tex]
What have you learned and how can you
apply your knowledge in rounding
decimal numbers to real-life situations?
Answer: With money or in jobs
Step-by-step explanation:
Some good places to practice rounding numbers is the grocery store, restaurants, or mall or while reading the newspaper or planning a party. For example, if you are at the grocery store with your child, you can ask him to round the prices of your items to the nearest dollar.
Grace looked at the thermometer outside and saw that it read -8 °F. Which is the best description for this temperature? A-8 °F is farther away from 0 °F than 8 °F is. B-8 °F is 8° below 0°. C-6 °F is colder than -8 °F. D-8 °F is warmer than 0 °F
Answer:
-8 °F is 8° below
Step-by-step explanation:
it's negative 8 so its 8 below
The sum of two numbers is 80. Their difference is 22.
Answer:
51 + 29
Step-by-step explanation:
please help me asap!!!
Answer:
Already answered it
Step-by-step explanation:
What is the value of x? Enter your answer in the box. x =
Answer:
x=20
Step-by-step explanation:
3x+50=6x-10
-3x=-60
x=20
A plane with the tailwind is 500 km/h. While going against the wind it is 410 km/h. What is the speed of the plane without wind?
Answer:
45
Step-by-step explanation:
Let the plane speed be x
Let the wind speed be y
x +y= 500.....equation 1
x -y= 410........equation 2
x + y= 500
-
x- y= 410
2x= 90
x= 90/2
x= 45
From equation 1, substitute 45 for x
x + y= 500
45 + y= 500
y = 500-45
x = 455
Hence the speed of the plane is 45
Which equation matches line p?
Answer:
line p matches with the first equation
Step-by-step explanation:
Find the sum of all the integers between -14 to 8
I will make you brainlest !!
Step-by-step explanation:
Hangg on.
There is a square root of -14 & 84.
a circle has a radius of 2x inches. if the radius is multiplied by a factor of 3/8. what is the new area of the circle
Answer:
(PI x 3/4x square) inches
Step-by-step explanation:
A of a circle = pi times radius squared
A = pi times 3/4x - that is 2x times 3/8
A = 3.14 (or whatever you use for pi) x 3/4 x inches square
Help&EXPLAIN
Don’t use for points or I’ll take it back and u will be reported
Answer:
103
Step-by-step explanation:
Every straight line's angle measurement is 180 degrees, so if one angle is 77 degrees, the other must be 103 degrees to equal 180. (77+103=180)
Hope this helps!
Find the value of x.
22°, 140°, x°
a.
18
b.
28
c.
8
d.
12
Step-by-step explanation:
I would assume the answer would be a. 18 assuming your trying to find the entire value of a triangle but have a missing value
(SAT Prep) Find the value of x
Sally pays $50.00 for a meal that costs $38.13. She tells the server to keep the difference as a tip. How much is the tip?
Answer:
11.87
Step-by-step explanation:
It just subtraction
A pack of cinnamon-scented pencils sells for $9.00. What is the sales tax rate if the total cost of the pencils
is $9.27?
The sales tax rate is
what is the point-slope form of the equation for the line with a slope of -2 that passes through the point (4,-6)
Answer:
[tex]y + 6 = -2 (x-4)[/tex]
Step-by-step explanation:
Point-slope formula is represented by the equation [tex]y-y_1 = m (x-x_1)[/tex]. When knowing a point a line crosses through and its slope, you can write an equation in this form. Substitute the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
The [tex]m[/tex] represents the slope of the line. Since we know the slope is -2, substitute -2 for [tex]m[/tex]. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of the point the line passes through. Since the line passes through (4, -6), substitute 4 for [tex]x_1[/tex] and -6 for [tex]y_1[/tex]. This gives the following answer and equation:
[tex]y-(-6) = -2 (x - (4))\\y + 6 = -2 (x-4)[/tex]
Answer:
y=-2x+2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-6)=-2(x-4)
y+6=-2(x-4)
y=-2x+8-6
y=-2x+2
Follow this link to view juan’s work. critique juan’s work by justifying correct solutions and by explaining any errors he made. for any errors made, provide and explain a correct response. be sure to explain each key aspect of the graph.
Answer:
Step-by-step explanation:
Let the exponential function given in the picture is,
f(x) = a(b)ˣ
Here, a = Initial value
b = Base value
x = Exponent
Since, the graph passes through the points (0, 1) and (1, 3)
For (0, 1),
1 = a(b)⁰
a = 1
For (1, 3),
3 = 1(b)¹
b = 3
Therefore, equation of the given function will be,
f(x) = (3)ˣ
Therefore, Initial value = 1
Base = 3
Asymptote (Horizontal) → y = 0
Vertical asymptote → None
Domain → (-∞, ∞) Or {x | x ∈ R}
Range → (0, ∞) Or {y | y > 0}
Therefore, answers given by Juan are incorrect.
what was the least of rows she could use?
PLEASE HELP! ASAP PLEASE!
Answer:
4, it's an isosceles trapezoid, so sides TP and RA should be equivalent
what does the word "of" mean?
A. in addition to
B. multiply by
C. divided by
Answer:
B. multiply by
Can I get help on this question? Please explain the process of how to solve it too.
Answer:
x = 13
y = 18.38
Step-by-step explanation:
tan 45 = x/13 (tangent = opposite / adjacent)
1 = x/13
multiply both sides by 13
x = 13
cos 45 = 13/y (cosine = adjacent / hypotenuse
0.7071 = 13/y
multiply both side by y
0.7071y = 13
divide both side by 0.7071
y = 18.38
Is it right???????????????
Answer:
No the awnser is no
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
There are limits on what the lengths can be. ... The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third.
What is 2 1/4 - 1 2/5 please help me
Answer: 17/20=0.85
Step-by-step explanation:
is gemini a bad sign be honest
Answer:
it depends on the person
Answer:
yea , we are tbh , we toxic . but we kinda lovable . we dont like large spaces . and we snakes
Step-by-step explanation:
which table represents a linear function?
Answer:
D. (2,7) (4,9) (6,11) (8,13)
Step-by-step explanation:
If you download the DESMOS app or go on their website (legit not fake) you will find that D will be a line function.
Hope this helped
answer for brainliest
Does anybody know the answer's to, 2,3, and 4?
Pls help extra points and mark brainlist
Answer:
A,B,D
Step-by-step explanation:
Laura buys an unfair coin online. The coin is supposed to land heads up 75% of the time. If this is true, what is the
probability that in 20 flips, the first 15 land heads up and the last 5 land tails up?
Answer:
C . (0.75) 15 x (0.25) 5
Step-by-step explanation:
Took the assignment in edge, it’s right
Its based off of the rule P(A and B) = P(A) x P(B) from multiplication rule for independent events.
The probability that in 20 flips, the first 15 land heads up and the last 5 land tails up is 0.000390625.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If the coin is supposed to land heads up 75% of the time, then the probability of getting heads on a single flip is 0.75 and the probability of getting tails is 0.25.
To find the probability that in 20 flips, the first 15 land heads up and the last 5 land tails up, you can use the formula for the probability of independent events:
P(A and B) = P(A) × P(B)
where A and B are independent events, and P(A) and P(B) are the probabilities of events A and B occurring, respectively.
In this case, the probability of the first 15 flips landing heads up is P(A) = 0.75¹⁵, and the probability of the last 5 flips landing tails up is P(B) = 0.25⁵.
Therefore, the probability that in 20 flips, the first 15 land heads up and the last 5 land tails up is:
P(A and B) = P(A) × P(B) = (0.75¹⁵) × (0.25⁵) = 0.000390625
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
Mary and Peter shared a cookie. Mary ate three tenths. Peter ate four tenths. How much is left?
Answer:
b.
Step-by-step explanation:
...
Answer:
3/10
Step-by-step explanation:
Mary ate 3/10
Peter ate 4/10
that equals 7/10
so 3/10 is left
PLEASE ANSWER! WOLL GIVE BRAINLIEST AND LOVE U FOREVER