Question

Read four digits from the random numbers table. note the number of odd digits in the selected numbers. Repeat the experiment 25 times. Obtain the probability distribution of the odd digits. Find mean and variance of the distribution

Answer 1

Ans. The toatal number of possible for digit numbers are

The odd numbers = 105

The even numbers = 105

Ley,

Y_{​​​​​​i} = 1 if number is odd = success

= 0 if number is even = failure

p = (Y_{​​​​​​i}​​​​​ = 1) = P( odd number) = 105/210 = 0.5

q = 1 - p = 0.5

Such types of experiment is known as bernoulBe trial.

Since this trial is repeated n = 25 times, each trail is independentl from each other and with constant probability p = 0.5 of success for each trail.

Let X = Y_{​​​​​​1} + Y_{​​​​​​2} + ....+ Y_​​25 has binomial distribution with parameters n = 25 and p = 0.5.

Mean = E(X) = np = 25*0.5 = 12.5

Variance= var(X) = npq = 25*0.5*0.5 = 6.25