Question

The random variable X takes only the values 0, ±1, ±2. In addition, it is known that P(-1 <X <2) 0.2 P(X = 0) = 0.05 PCI 1) = 0.35 P(X 2) = P(X = 1 or-1) (a) Find the probability distribution of X (b) Compute E[X]

Answer 1

x takes following values

-2, -1, 0, 1, 2

P(-1<x<2) = P(X=0) + P(X=1) = 0.2

P(X=0) = 0.05

tis implies

P(X=1) = 0.2 - 0.05 = 0.15

P(X=-1) + P(X=0) + P(X=1) = 0.35

this implies P(X=-1) = 0.35-0.2 = 0.15

$P(X\ge 2) = P(X=1 \;or X=-1)$

P(X=2) = P(X=1) + P(X=-1) = 0.15 + 0.15

P(X=2) = 0.15

x P(x) xP(x)   
-2.0 | 0.5 | -1.0
-1.0 | 0.15 | -0.15
0.0 | 0.05 | 0.0  
1.0 | 0.15 | 0.15
2.0 | 0.15 | 0.3  
$\sum x.P(x) = -0.7$
Since we know that,

M ean = 〉 .r.P(x)--0.7