Probability Distribution of Discrete Random Variables

The probability distribution of a discrete r.v.X is as follows.

Complete the following activity.

Solution: Since `sum"p"_"i"` = 1

P(X ≤ 4) = `square + square + square + square = square`

Solve the following :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

The person on the high protein diet is interested gain of weight in a week.

Solve the following problem :

Find the expected value and variance of the r. v. X if its probability distribution is as follows.

Find k, if the following function represents p.d.f. of r.v. X.

f(x) = kx(1 – x), for 0 < x < 1 and = 0, otherwise.

Also, find `P(1/4 < x < 1/2) and P(x < 1/2)`.

It is known that error in measurement of reaction temperature (in 0° c) in a certain experiment is continuous r.v. given by

f (x) = `x^2 /3` , for –1 < x < 2 and = 0 otherwise

 Verify whether f (x) is p.d.f. of r.v. X.

State if the following is not the probability mass function of a random variable. Give reasons for your answer

Solve the following problem :

The probability distribution of a discrete r.v. X is as follows.

Determine the value of k.

The probability distribution of X is as follows:

Find:

1. k
2. P[X < 2]
3. P[X ≥ 3]
4. P[1 ≤ X < 4]
5. P(2)