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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Choose the correct option from the given alternative: If p.m.f. of a d.r.v. X is P (X = x) = (cx5)25 , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise If a = P (X ≤ 2) and b = P (X ≥ 3), then E (X ) = - Mathematics and Statistics

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प्रश्न

Choose the correct option from the given alternative:

If p.m.f. of a d.r.v. X is P (X = x) = `((c_(x)^5 ))/2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise If a = P (X ≤ 2) and b = P (X ≥ 3), then E (X ) =

पर्याय

  • a < b

  • a > b

  • a = b

  • a + b

MCQ
रिकाम्या जागा भरा

उत्तर

If p.m.f. of a d.r.v. X is P (X = x) = `((c_(x)^5 ))/2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise If a = P (X ≤ 2) and b = P (X ≥ 3), then E (X ) = a = b

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Probability Distribution of Discrete Random Variables
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Probability Distributions - Miscellaneous Exercise 1 [पृष्ठ २४२]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
पाठ 7 Probability Distributions
Miscellaneous Exercise 1 | Q 5 | पृष्ठ २४२

संबंधित प्रश्‍न

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

Z 3 2 1 0 −1
P(Z) 0.3 0.2 0.4 0 0.05

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

A random variable X has the following probability distribution:

X 0 1 2 3 4 5 6 7
P(X) 0 k 2k 2k 3k k2 2k2 7k2 + k

Determine:

  1. k
  2. P(X < 3)
  3. P( X > 4)

Find the mean number of heads in three tosses of a fair coin.


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 )


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


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

f (x) = kx, for 0 < x < 2 and = 0 otherwise, Also find P `(1/ 4 < x < 3 /2)`.


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)`.


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(0.5 ≤ x ≤ 1.5)


Find expected value and variance of X, the number on the uppermost face of a fair die.


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

f(x) = `{(kx,  "for"  0 < x < 2),(0,  "otherwise."):}`

Also find `"P"[1/4 < "X" < 1/2]`


Choose the correct alternative :

X: is number obtained on upper most face when a fair die….thrown then E(X) = _______.


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


Choose the correct alternative :

If X ∼ B`(20, 1/10)` then E(X) = _______


State whether the following is True or False :

If P(X = x) = `"k"[(4),(x)]` for x = 0, 1, 2, 3, 4 , then F(5) = `(1)/(4)` when F(x) is c.d.f.


Solve the following problem :

The p.m.f. of a r.v.X is given by

`P(X = x) = {(((5),(x)) 1/2^5", ", x = 0", "1", "2", "3", "4", "5.),(0,"otherwise"):}`

Show that P(X ≤ 2) = P(X ≤ 3).


Solve the following problem :

The following is the c.d.f of a 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 the probability distribution of X and P(–1 ≤ X ≤ 2).


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)`

Solve the following problem :

Let the p. m. f. of the r. v. X be

`"P"(x) = {((3 - x)/(10)", ","for"  x = -1", "0", "1", "2.),(0,"otherwise".):}`
Calculate E(X) and Var(X).


Solve the following problem :

Let X∼B(n,p) If n = 10 and E(X)= 5, find p and Var(X).


Solve the following problem :

Let X∼B(n,p) If E(X) = 5 and Var(X) = 2.5, find n and p.


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


If a d.r.v. X has the following probability distribution:

X –2 –1 0 1 2 3
P(X = x) 0.1 k 0.2 2k 0.3 k

then P(X = –1) is ______


Find mean for the following probability distribution.

X 0 1 2 3
P(X = x) `1/6` `1/3` `1/3` `1/6`

Choose the correct alternative:

f(x) is c.d.f. of discete 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 values of discrete r.v. are generally obtained by ______


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


The following function represents the p.d.f of a.r.v. X

f(x) = `{{:((kx;, "for"  0 < x < 2, "then the value of K is ")),((0;,  "otherwise")):}` ______ 


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.


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)


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