NCERT Class 12-Mathematics: Chapter – 13 Probability Part 9 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 24:

Consider the probability distribution of a random variable X:

Consider the Probability Distribution

Calculate (i)

(ii) Variance of X.

Answer:

(i)

(ii)

Question 25:

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

The Probability Distribution

(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.

The Probability Distribution

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

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:

The Probability Distribution of ′ the Number of Ones Seen