CBSE Class 12 Applied Mathematics — Probability Distributions

Let X be a discrete random variable, then the variance of X is :

If 'm' is the mean of a Poisson distribution, then its variance is given by :

The total area under a standard normal curve is :

(a) For a Poisson distribution, if mean (m) = 1, then find $P(r = 1)$. OR (b) Find the mean and standard deviation of the Binomial distribution $B\left(4, \frac{1}{3}\right)$.

(a) Two cards are drawn at random and one by one with replacement from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of aces. Also, find its mean and variance. OR (b) It is given that 2% of the screws manufactured by a company are defective. Use Poisson distribution to find the probability that a packet of 100 screws contains (i) no defective screw, (ii) one defective screw.