Question

11. Using the probability distribution listed below, (... 2 0.30 3 0.24 4 0.10 P(x) 0.10 0.26 a. Find the mean, variance and standard deviation b. Find P(x is no more than 3) c. Find P(x is at least 2) d. Find P(x<2 or x>2) e. Find P(x is less than 3)

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
0	0.1	0	0
1	0.26	0.26	0.26
2	0.3	0.6	1.2
3	0.24	0.72	2.16
4	0.1	0.4	1.6
Sum	1	1.98	5.22

(a)

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

$\mu$ = 1.98

Variance = $\sigma$ ²

= $\sum$ X ² * P(X) - $\mu$ ²

= 5.22 - 1.98²

= 1.2996

standard deviation = 1.14

(b)

P(x is no more than 3) = P(1) + P(2) + P(3) = 0.10 + 0.26 + 0.30 = 0.66

(c)

P(x is at least 2) = P(2) + P(3) + P(4) = 0.30 + 0.24 + 0.10 = 0.64

(d)

P(x < 2 or x > 2) = 1 - P(x = 2) = 1 - 0.30 = 0.70

(e)

P(x is less than 3) = P(1) + P(2) = 0.10 + 0.26 = 0.36