Question

(6).
The p. m. f. of a random variable is as follows
X = x
1
2
3
4
4
9
16
P(x)
1/30
1/30
1/30
1/30
Find Mean and the Variance.​

Answer 1

Step-by-step explanation:

mean=summation of xipi=1/30+8/30+27/30+64/30

=100/30=10/3=3.33

variance =summation xi²pi-(summation xipi)²

=59/5-(10/3)²

=59/5-100/9

=531-50/45

=31/45

=0.6888

Answer 2

Answer:

Mean $=3.33,$ Variance $=0.6888.$

Step-by-step explanation:

Mean $=$ ∑$x_ip_i=$ $\frac{1}{30}+\frac{8}{30}+\frac{27}{30}+\frac{64}{30}=\frac{100}{30}=3.33$

Variance $=$ ∑$x^2_ip_i-($∑$x_ip_i)^2$

               $=$ $\frac{59}{5} -(\frac{10}{3})^2$

               $=$ $531-\frac{50}{45}=0.6888$