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  • Provide solution for RD Sharma maths class 12 chapter 31 Mean and Variance of a Random Variable exercise 31.1 question 13 maths textbook solution

Provide solution for RD Sharma maths class 12 chapter 31 Mean and Variance of a Random Variable exercise 31.1 question 13 maths textbook solution

Answers (1)

Answer: 

X 14 15 16 17 18 19 20 21
P\left ( X \right ) \frac{2}{15} \frac{1}{15} \frac{2}{15} \frac{1}{5} \frac{1}{15} \frac{2}{15} \frac{1}{5} \frac{1}{15}


Hint: Use frequency table

Given: A class has 15 students whose ages are 14,17,15,14,21,19,20,16,18,17,20,17,16,19 and 20 years respectively. One student is selected in such a manner that each has the same chance of being selected and the age x of the selected student is recorded. We have to find the probability distribution of the random variable x

Solution:

Note: many of the time while solving such simple problems we make a mistake in counting so at first, we should make a frequency table which tells us no of students in the class of the same age.

This makes our interpretation easier.

\therefore Frequency distribution table for age and number of student is:

Age 14 15 16 17 18 19 20 21

Number

of

student

 2 1 2 3 1 2 3 1

X represents the age of a random student

\therefore can take value 14, 15, 16,17,18,19,20 or 21

Total no. of students in class = 15

Using the above frequency table, we can easily see a total number of students of a particular age, and hence we can find probability easily.

\begin{aligned} &\left\{\text { As probability }=\frac{\text { no of favourable outcome }}{\text { total no of outcome }}\right\} \\ &P(x=14)=\frac{2}{15} \end{aligned}

Similarly,

\begin{aligned} &P(x=15)=\frac{1}{15} ; \\ &P(x=16)=\frac{2}{15} \\ &P(x=17)=\frac{3}{15}=\frac{1}{5} \\ &P(x=18)=\frac{1}{15} \\ \end{aligned}

\begin{aligned} &P(x=19)=\frac{2}{15} \\ &P(x=20)=\frac{3}{15}=\frac{1}{5} \\ &P(x=21)=\frac{1}{15} \end{aligned}

\therefore Required Probability distribution is

X 14 15 16 17 18 19 20 21
P\left ( X \right ) \frac{2}{15} \frac{1}{15} \frac{2}{15} \frac{1}{5} \frac{1}{15} \frac{2}{15} \frac{1}{5} \frac{1}{15}

 

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