Question

The probability distribution of a random variable X is: | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | k | 2k | k | 0.1 | where k is some unknown constant. The probability that the random variable X takes the value 2 is:

The random variable X has the following probability distribution where a and b are some constants : | X | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | P(X) | 0.2 | a | a | 0.2 | b | If the mean E(X) = 3, then find values of a and b and hence determine P(X ≥ 3).

An urn contains 3 red and 2 white marbles. Two marbles are drawn one by one with replacement from the urn. Find the probability distribution of the number of white balls. Also, find the mean of the number of white balls drawn.

A salesman receives a commission for each sale he makes together with a fixed daily income. The number of sales he makes in a day along with their probabilities are given in the table below : | X | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | P(X) | 0.42 | 3k | 0.3 | 0.05 | 2k | 0.03 | His daily income Y (in ₹) is given by : Y = 800X + 50