English

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 = - Mathematics and Statistics

Advertisements
Advertisements

Question

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 =

Options

  • 1

  • `1/2`

  • `1/3`

  • `1/4`

MCQ
Fill in the Blanks

Solution

If P (X < a) = P (X > a), then a = `1/2`

shaalaa.com
Probability Distribution of Discrete Random Variables
  Is there an error in this question or solution?
Chapter 7: Probability Distributions - Miscellaneous Exercise 1 [Page 241]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
Chapter 7 Probability Distributions
Miscellaneous Exercise 1 | Q 1 | Page 241

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 3 4
P(X) 0.1 0.5 0.2 − 0.1 0.2

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

0 -1 -2
P(X) 0.3 0.4 0.3

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 ( 1 < x < 2 )


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)


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.


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

Find probability that X is negative


Choose the correct option from the given alternative:

If the p.d.f of a.c.r.v. X is f (x) = 3 (1 − 2x2 ), for 0 < x < 1 and = 0, otherwise (elsewhere) then the c.d.f of X is F(x) =


Choose the correct option from the given alternative :

If p.m.f. of a d.r.v. X is P (x) = `c/ x^3` , for x = 1, 2, 3 and = 0, otherwise (elsewhere) then E (X ) =


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.


Solve the following :

The following probability distribution of r.v. X

X=x -3 -2 -1 0 1 2 3
P(X=x) 0.05 0.1 0.15 0.20 0.25 0.15 0.1

Find the probability that

X is positive


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

P (–1 ≤ X ≤ 2)


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

x = x 1 2 3 4 5 6
P[x=x] k 2k 3k 4k 5k 6k

(i) Determine the value of k.

(ii) Find P(X≤4), P(2<X< 4), P(X≥3).


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)


Find the probability distribution of number of number of tails in three tosses of a coin


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) = _______ .


The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.


X is r.v. with p.d.f. f(x) = `"k"/sqrt(x)`, 0 < x < 4 = 0 otherwise then x E(X) = _______


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


Fill in the blank :

E(x) is considered to be _______ of the probability distribution of x.


State whether the following is True or False :

x – 2 – 1 1 2
P(X = x) 0.2 0.3 0.15 0.25 0.1

If F(x) is c.d.f. of discrete r.v. X then F(–3) = 0


State whether the following is True or False :

If p.m.f. of discrete r.v. X is

x 0 1 2
P(X = x) q2 2pq p2 

then E(x) = 2p.


Solve the following problem :

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

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

Find P(X ≤ 4), P(2 < X < 4), P(X ≤ 3).


Solve the following problem :

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

x 1 2 3
P(X = x) `(1)/(5)` `(2)/(5)` `(2)/(5)`

If a d.r.v. X takes values 0, 1, 2, 3, … with probability P(X = x) = k(x + 1) × 5–x, where k is a constant, then P(X = 0) = ______


If the p.m.f. of a d.r.v. X is P(X = x) = `{{:(x/("n"("n" + 1))",", "for"  x = 1","  2","  3","  .... "," "n"),(0",", "otherwise"):}`, then E(X) = ______


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

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

then Var(x) = ______


E(x) is considered to be ______ of the probability distribution of x.


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 ≥ 3) = `square - square - square  = square`


Using the following activity, find the expected value and variance of the r.v.X if its probability distribution is as follows.

x 1 2 3
P(X = x) `1/5` `2/5` `2/5`

Solution: µ = E(X) = `sum_("i" = 1)^3 x_"i""p"_"i"`

E(X) = `square + square + square = square`

Var(X) = `"E"("X"^2) - {"E"("X")}^2`

= `sum"X"_"i"^2"P"_"i" - [sum"X"_"i""P"_"i"]^2`

= `square - square`

= `square`


Given below is the probability distribution of a discrete random variable x.

X 1 2 3 4 5 6
P(X = x) K 0 2K 5K K 3K

Find K and hence find P(2 ≤ x ≤ 3)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×