Q29 of 77 Page 32

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)

The key point to solve the problem:


If a probability distribution is given then as per its definition, Sum of probabilities associated with each value of a random variable of given distribution is equal to 1


i.e. ∑(pi) = 1


Given distribution is :


(i)


∴




∴ (i)


(ii) P(X>2) = P(X = 3) =


∴ P(X>2) =


P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = = …(ii)


(iii) ∴ P(X>2) + P(X≤ 2) =


More from this chapter

All 77 →
27

From a lot of 10 bulbs, which includes 3 detectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.

 28

Four balls are to drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red balls drawn, find the probability distribution of X.

 30

Let X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that


Where k is a positive constant.


Find the value of k. Also, find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.

 1

Find the mean and standard deviation of each of the following probability distributions: