English

If p.m.f. of r.v. X is given below. x 0 1 2 P(x) q2 2pq p2 then Var(x) = ______ - Mathematics and Statistics

Advertisements
Advertisements

Question

If p.m.f. of r.v. X is given below.

x 0 1 2
P(x) q2 2pq p2

then Var(x) = ______

Options

  • p2

  • q2

  • pq

  • 2pq

MCQ
Fill in the Blanks

Solution

If p.m.f. of r.v. X is given below.

x 0 1 2
P(x) q2 2pq p2

then Var(x) = 2pq

shaalaa.com
Probability Distribution of Discrete Random Variables
  Is there an error in this question or solution?
Chapter 2.8: Probability Distributions - Q.1

APPEARS IN

RELATED QUESTIONS

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

X 0 1 2
P(X) 0.4 0.4 0.2

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

X 0 1 2
P(X) 0.1 0.6 0.3

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

Y −1 0 1
P(Y) 0.6 0.1 0.2

Find expected value and variance of X for the following p.m.f.

x -2 -1 0 1 2
P(X) 0.2 0.3 0.1 0.15 0.25

The following is the p.d.f. of r.v. X:

f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise.

 P(x > 2)


Suppose that X is waiting time in minutes for a bus and its p.d.f. is given by f(x) = `1/5`, for 0 ≤ x ≤ 5 and = 0 otherwise.

Find the probability that the waiting time is more than 4 minutes.


Choose the correct option from the given alternative :

P.d.f. of a.c.r.v X is f (x) = 6x (1 − x), for 0 ≤ x ≤ 1 and = 0, otherwise (elsewhere)

If P (X < a) = P (X > a), then a =


Solve the following :

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

Amount of syrup prescribed by physician.


The following is the c.d.f. of r.v. X:

X −3 −2 −1 0 1 2 3 4
F(X) 0.1 0.3 0.5 0.65 0.75 0.85 0.9 1

Find p.m.f. of X.
i. P(–1 ≤ X ≤ 2)
ii. P(X ≤ 3 / X > 0).


Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f

f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise.

Calculate: P(x≤1)


Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f

f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise. Calculate: P(x ≥ 1.5)


Given that X ~ B(n, p), if n = 10 and p = 0.4, find E(X) and Var(X)


Given that X ~ B(n,p), if n = 10, E(X) = 8, find Var(X).


F(x) is c.d.f. of discrete r.v. X whose distribution is

Xi – 2 – 1 0 1 2
Pi 0.2 0.3 0.15 0.25 0.1

Then F(–  3) = _______ .


If F(x) is distribution function of discrete r.v.X with p.m.f. P(x) = `k^4C_x` for x = 0, 1, 2, 3, 4 and P(x) = 0 otherwise then F(–1) = _______


Solve the following problem :

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

x – 1 0 1
P(X = x) `(1)/(5)` `(2)/(5)` `(2)/(5)`

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

x 1 2 3 4 5 6
P(X = x) k 2k 3k 4k 5k 6k

Complete the following activity.

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

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


The probability distribution of X is as follows:

x 0 1 2 3 4
P[X = x] 0.1 k 2k 2k k

Find

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

The p.m.f. of a random variable X is as follows:

P (X = 0) = 5k2, P(X = 1) = 1 – 4k, P(X = 2) = 1 – 2k and P(X = x) = 0 for any other value of X. Find k.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×