Question

X	5	6	7	8
P(X)	1/16	5/8	1/4	1/16

i.

Is this probability distribution of random variable X valid or legitimate? Explain?

ii.

iii.

Find the expected value (μ) of this distribution.

Find the standard deviation (σ) of thisdistribution.

Answer 1

i)

This is valid probability distribution when P(X) = 1

Now,

P(X) = 1/16 + 5/8 + 1/4 + 1/16 = 1

Therefore, this is valid probability distribution.

b)

E(X) = X * P(X)

= 5 * 1/16 + 6 * 5/8 + 7 * 1/4 + 8 * 1/16

= 6.3125

c)

Standard deviation = X² * P(X) - [ E(X)]²

= [ 5² * 1/16 + 6² * 5/8 + 7² * 1/4 + 8² * 1/16 ] - 6.3125²

= 0.6818