Question

Let X be a random variable with PMF px(x) = { x^2/a, if x = -3, -2, -1, 0, 1, 2, 3, 0, otherwise. (a) Find a and E[X]. (b) What is the PMF of the random variable Z = (X - E[X])^2 ? (c) Using the result from part (b), find the variance of X. (d) Find the variance of X using the formula var(X) = sum_x (x - E[X])^2 px(x).

          Let X be a random variable with PMF
px(x) = {
x^2/a, if x = -3, -2, -1, 0, 1, 2, 3,
0, otherwise.
(a) Find a and E[X].
(b) What is the PMF of the random variable Z = (X - E[X])^2 ?
(c) Using the result from part (b), find the variance of X.
(d) Find the variance of X using the formula var(X) = sum_x (x - E[X])^2 px(x).

Let X be a random variable with PMF
px(x) =
x^2/a, if x = -3, -2, -1, 0, 1, 2, 3,
0, otherwise.
(a) Find a and E[X].
(b) What is the PMF of the random variable Z = (X - E[X])^2 ?
(c) Using the result from part (b), find the variance of X.
(d) Find the variance of X using the formula var(X) = sumx (x - E[X])^2 px(x).

Added by Sharon C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

06/16/2023

Step 1

Since the PMF must sum to 1, we have: $$ \sum_{i=-3}^{3} \frac{i^2}{a} = 1 $$ $$ \frac{(-3)^2 + (-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2}{a} = 1 $$ $$ \frac{50}{a} = 1 $$ So, we have: $$ a = 50 $$ Now, let's find the expected value E[X]: $$ E[X] = Show more…

Show all steps

Thanks for your feedback!

Let X be a random variable with PMF px(x) = { x^2/a, if x = -3, -2, -1, 0, 1, 2, 3, 0, otherwise. (a) Find a and E[X]. (b) What is the PMF of the random variable Z = (X - E[X])^2 ? (c) Using the result from part (b), find the variance of X. (d) Find the variance of X using the formula var(X) = sum_x (x - E[X])^2 px(x).