Question

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)...

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)

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Here,

a)

We know,

So,

On comparing both sides, we get,

So,

Also,

b)

We know,

So,

On comparing both sides, we get,

So,

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X be a discrete random variable with probability mass function (pmf) P (X = k)...
Let X be a discrete random variable with probability mass function (pmf) P (X = k) = C *ln(k) for k = e; e^2 ; e^3 ; e^4 , and C > 0 is a constant. (a) Find C. (b) Find E(ln X). (c) Find Var(ln X).
1. Let X be a discrete random variable with the probability mass function P(x) = kx2...
1. Let X be a discrete random variable with the probability mass function P(x) = kx2 for x = 2, 3, 4, 6. (a) Find the appropriate value of k. (b) Find P(3), F(3), P(4.2), and F(4.2). (c) Sketch the graphs of the pmf P(x) and of the cdf F(x). (d) Find the mean µ and the variance σ 2 of X. [Note: For a random variable, by definition its mean is the same as its expectation, µ = E(X).]
Let descrete random variable X~Poisson(6). Find: Probability P(X=5) Probability P(X=2) Probability P(X<3) Probability P(X>6) μX σX
Let descrete random variable X~Poisson(6). Find: Probability P(X=5) Probability P(X=2) Probability P(X<3) Probability P(X>6) μX σX
Consider a discrete random variable X with probability mass function P(X = x) = p(x) =...
Consider a discrete random variable X with probability mass function P(X = x) = p(x) = C/3^x, x = 2, 3, 4, . . . a. Find the value of C. b. Find the moment generating function MX(t). c. Use your answer from a. to find the mean E[X]. d. If Y = 3X + 5, find the moment generating function MY (t).
A random variable X has its probability function given by x 0 1 2 3 4...
A random variable X has its probability function given by x 0 1 2 3 4 f(x) 0.3c 0.1c c 0.2c 0.4c a) Find c and F(x), the cumulative distribution function for X (for all real values of X). b) Find the probabilities of the event X = 6 and the event X >= 4. c) Find P(1 < X <= 4) and P(1 < X <= 4 | X <= 3).
Let X be a random variable with density function f(x) = 2 5 x for x...
Let X be a random variable with density function f(x) = 2 5 x for x ∈ [2, 3] and f(x) = 0, otherwise. (a) (6 pts) Compute E[(X − 2)3 ] without attempting to find the density function of Y = (X − 2)3 . (b) (6 pts) Find the density function of Y = (X − 2)3
Suppose X is a discrete random variable with probability mass function given by p (1) =...
Suppose X is a discrete random variable with probability mass function given by p (1) = P (X = 1) = 0.2 p (2) = P (X = 2) = 0.1 p (3) = P (X = 3) = 0.4 p (4) = P (X = 4) = 0.3 a. Find E(X^2) . b. Find Var (X). c. Find E (cos (piX)). d. Find E ((-1)^X) e. Find Var ((-1)^X)
Let X be a normally distributed random variable with mean 5. 1. If P(4 ≤ X...
Let X be a normally distributed random variable with mean 5. 1. If P(4 ≤ X ≤ 4.6) = .240, find P(5.4 ≤ X ≤ 6). 2. Suppose P(X ≤ k) = .5 for some number k. What is the value of k? 3. Suppose P(X ≤ ℓ.) = .841, for some mystery value ℓ.. Approximately how many standard deviations above or below the mean is the value ℓ.?
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0...
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0 < ? < 2. (a) Find the constant c. (b) Find the cumulative distribution function (CDF) of X. (c) Find P(X < 0.5), and P(X > 1.0). (d) Find E(X), Var(X) and E(X5 ).
Q6/   Let X be a discrete random variable defined by the following probability function x 2...
Q6/   Let X be a discrete random variable defined by the following probability function x 2 3 7 9 f(x) 0.15 0.25 0.35 0.25 Give   P(4≤  X < 8) ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Q7/ Let X be a discrete random variable defined by the following probability function x 2 3 7 9 f(x) 0.15 0.25 0.35 0.25 Let F(x) be the CDF of X. Give  F(7.5) ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Q8/ Let X be a discrete random variable defined by the following probability function : x 2 6...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT