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NCERT Class 12- Mathematics: Chapter β 13 Probability Part 9
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: