Question

1. Discrete Random Variable.     The random variable x has the discrete probability distribution shown here:

x	-2	-1	0	1	2
p(x)	0.1	0.15	0.4	0.3	0.05

1. Find P(-1<=x<=1)  
2. Find P(x<2)
3. Find the expected value (mean) of this discrete random variable.
4. Find the variance of this discrete random variable

Answer 1

Solution :

(a)

P(-1 $\leq$ x $\leq$ 1) = P(-1) + P(0) + P(1) = 0.15 + 0.4 + 0.3 = 0.85

(b)

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

=0.95

(c)

x	P(x)	x * P(x)	x2 * P(x)
-2	0.1	-0.2	0.4
-1	0.15	-0.15	0.15
0	0.4	0	0
1	0.3	0.3	0.3
2	0.05	0.1	0.2
Sum	1	0.05	1.05

c)

Expected value =

Mean = $\mu$ = $\sum$ X * P(X) = 0.05

variance

= $\sum$ X ² * P(X) - $\mu$ ²

= 1.05 - (-0.05)²

= 1.0475