Determine the mean and variance of the random variable with the following probability mass function. f (x) = (1/2)(x/5), x = 1, 2, 3, 4

Determine:
a. P(X = 2)
b. P(X = 3)
c. P(X > 2.5)
d. P(X = 1)
e. Mean
f. Variance.

a. P(X = 2) = 0.2

b. P(X = 3) = 0.3

c. P(X > 2.5) = 0.7

d. P(X = 1) = 0.1

e. Mean = 3

f. Variance = 1

Step-by-step explanation:

As given,

Probability mass function (pmf) =

Now,

a. P(X = 2) = = 0.2

b. P(X = 3) = = 0.3

c. P(X > 2.5) = P(X = 3) + P(X = 4) = = 0.3 + 0.4 = 0.7

d. P(X = 1) = = 0.1

e. Mean = E(X) = = 0.1 + 0.4 + 0.9 + 1.6 = 3

f. Variance = E(X²) - [ E(X) ]² =  - [3]²

                                             = 0.1 + 0.8 + 2.7 + 6.4 - 9

                                             = 10 - 9 = 1

∴ we get

a. P(X = 2) = 0.2

b. P(X = 3) = 0.3

c. P(X > 2.5) = 0.7

d. P(X = 1) = 0.1

e. Mean = 3

f. Variance = 1