Probability — Class 12 Maths Solution

ncert exercise SA NCERT,EX.13.4,Q.1,Page.569
Question

State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

(i) $\begin{array}{l}X\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\\P(X)\,\,\,\,\,\,\,\,\,\,\,0.4\,\,\,\,\,\,\,\,\,\,\,0.4\,\,\,\,\,\,\,\,\,\,\,0.2\end{array}$

(ii) $\begin{array}{l}X\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,3\\P(X)\,\,\,\,\,\,\,\,\,\,\,0.4\,\,\,\,\,\,\,\,\,\,\,0.4\,\,\,\,\,\,\,\,\,\,\,0.2\,\,\,\,\,\,\,\,\, - 0.1\end{array}$

(iii) $\begin{array}{l}Y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\\P(X)\,\,\,\,\,\,\,\,\,\,\,0.6\,\,\,\,\,\,\,\,\,\,\,\,\,0.1\,\,\,\,\,\,\,\,\,\,\,0.2\end{array}$

(iv) $\begin{array}{l}Z\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,0\\P(X)\,\,\,\,\,\,\,\,\,\,\,0.3\,\,\,\,\,\,\,\,\,\,\,0.2\,\,\,\,\,\,\,\,\,\,\,0.4\,\,\,\,\,\,\,\,\, - 0.1\end{array}$

Step-by-step Solution

.: (i) This distribution is probability distribution, because sum of probabilities is one

(ii) This distribution is not a probability distribution, because probability can never be negative

(iii) This distribution is not a probability distribution, because sum of probabilities is less than one

(iv) This distribution is not a probability distribution, because sum of probabilities is more than one.

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Probability. Curated by Sachin Sharma. Free for all students.