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

(i) Determine the value of k.

(ii) Determine P (X ≤ 2) and P (X > 2)

(iii) Find P (X ≤ 2) + P (X > 2).

A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?

Consider the probability distribution of a random variable X:

Calculate (i) (ii) Variance of X.

For the following probability distribution determine standard deviation of the random variable X.

A biased die is such that P (4) = 1/10 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.