# NCERT Class 12-Mathematics: Chapter –13 Probability Part 9

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**Question 24:**

Consider the probability distribution of a random variable X:

Calculate (i)

(ii) Variance of X.

**Answer:**

(i)

(ii)

**Question 25:**

The probability distribution of a random variable X is given below:

(i) Determine the value of *.*

(ii) Determine and

(iii) Find .

**Answer:**

(i)

(ii)

(iii)

**Question 26:**

For the following probability distribution determine standard deviation of the random variable X.

**Answer:**

**Question 27:**

A biased die is such that and other scores being equally likely. The die is tossed twice. If X is the ‘number of fours seen’, find the variance of the random variable X.

**Answer:**

Since,

On tossing two die,

Also,

So,

Thus, we get following table

**Question 28:**

A die is thrown three times. Let be ‘the number of twos seen’. Find the expectation of .

**Answer:**

We have,

So, on throwing a die three times, we will have .

We know that,

**Question 29:**

Two biased dice are thrown together. For the first die , the other scores being equally likely while for the second die, and the other scores are equally likely. Find the probability distribution of ‘the number of ones seen’.

**Answer:**