Suppose X has the following p.m.f.f(x) = cx2, x= - 1,0,1for a constant c.A. Determine the constant c so that f(x) satisfies the conditions of being a p.m.f.B. Compute E(X):C. Compute E(X2).D. Compute Var(X):E. Compute E((X + 1)(X – 2))

Name: Suppose X has the following p.m.f.f(x) = cx2, x= - 1,0,1for a constan
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Description: Suppose X has the following p.m.f.f(x) = cx2, x= - 1,0,1for a constant c.A. Determine the constant c so that f(x) satisfies the conditions of being a p.m.f.B. Compute E(X):C. Compute E(X2).D. Compute Var(X):E. Compute E((X + 1)(X – 2))

Answered: Suppose X has the following p.m.f. f(x)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose X has the following p.m.f.
f(x) = cx2, x= - 1,0,1
for a constant c.
A. Determine the constant c so that f(x) satisfies the conditions of being a p.m.f.
B. Compute E(X):
C. Compute E(X2).
D. Compute Var(X):
E. Compute E((X + 1)(X – 2))

Expert Solution

Step 1

For any probability distribution to be valid, the sum of probabilities over the range of the random variable must be equal to one.

(A) Compute the value of the constant c using the formula:

$\sum_{x = - 1, 0, 1} c x^{2} = 1$

$c [{(- 1)}^{2} + {(0)}^{2} + {(1)}^{2}] = 1 c [1 + 0 + 1] = 1 c [2] = 1 c = \frac{1}{2}$

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