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If r.v. X assumes the values 1, 2, 3, …….., 9 with equal probabilities, then E(X) = 5 - Mathematics and Statistics

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प्रश्न

If r.v. X assumes the values 1, 2, 3, …….., 9 with equal probabilities, then E(X) = 5

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is True

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Probability Distribution of a Continuous Random Variable
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2.8: Probability Distributions - Q.3

संबंधित प्रश्न

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 0.10 0.15 0.20 0.25 0.15 0.1

Find the probability that

X is non-negative


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

f(x) = `{(x/(8),  "for"  0 < x < 4),(0,  "otherwise."):}`

Find P(1 < X < 2),


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

f(x) = `{(x/(8),  "for"  0 < x < 4),(0,  "otherwise."):}`

Find P(X > 2)


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

f(x) = `{(0.5x, "for" 0 ≤ x ≤ 2),(0, "otherwise".):}`
Calculate : P(X ≥ 1.5)


Suppose X is the waiting time (in minutes) for a bus and its p. d. f. is given by

f(x) = `{(1/5,  "for"  0 ≤ x ≤ 5),(0,  "otherwise"):}`

Find the probability that waiting time is between 1 and 3 minutes.


Suppose error involved in making a certain measurement is a continuous r. v. X with p.d.f.

f(x) = `{("k"(4 - x^2), "for" -2 ≤ x ≤ 2),(0, "otherwise".):}`
compute P(–1 < X < 1)


Following is the p. d. f. of a continuous r.v. X.

f(x) = `{(x/8,  "for"  0 < x < 4),(0,  "otherwise".):}`
Find expression for the c.d.f. of X.


The p.d.f. of a continuous r.v. X is

f(x) = `{((3x^2)/(8), 0 < x < 2),(0, "otherwise".):}`
Determine the c.d.f. of X and hence find P(X < –2)


If a r.v. X has p.d.f f(x) = `{("c"/x","  1 < x < 3"," "c" > 0),(0","  "otherwise"):}` 
Find c, E(X), and Var(X). Also Find F(x).


Choose the correct alternative :

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

x 0 1 2
P(x) q2 2pq p2 

Then Var(X) = _______


Choose the correct alternative :

Given p.d.f. of a continuous r.v.X as f(x) =  `x^2/(3)` for –1 < x < 2 = 0 otherwise then F(1) = _______.


Fill in the blank :

If x is continuous r.v. and F(xi) = P(X ≤ xi) = `int_(-oo)^(oo) f(x)*dx` then F(x) is called _______


Solve the following problem :

Suppose error involved in making a certain measurement is a continuous r.v.X with p.d.f.

f(x) = `{("k"(4 - x^2), "for" -2 ≤ x ≤ 2),(0, "otherwise".):}`
Compute P(X < – 0.5 or X > 0.5)


Solve the following problem :

The p.d.f. of the r.v. X is given by

f(x) = `{("k"/sqrt(x), "for"  0 < x < 4.),(0, "otherwise".):}`
Determine k, the c.d.f. of X, and hence find P(X ≤ 2) and P(X ≥ 1).


The values of continuous r.v. are generally obtained by ______


State whether the following statement is True or False:

If f(x) = `{:("k"x  (1 - x)",", "for"  0 < x < 1),(= 0",", "otherwise"):}`
is the p.d.f. of a r.v. X, then k = 12


For the following probability density function of a random variable X, find P(X < 1).

`{:(f(x) = (x + 2)/18,";"  "for" -2 < x < 4),(               = 0,","  "otherwise"):}`


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

f(x) = `{:(kx^2(1 - x)",", "for"  0 < x < 1),(0",", "otherwise"):}`


If the p.d.f. of X is

f(x) = `x^2/18,   - 3 < x < 3`

      = 0,        otherwise

Then P(X < 1) is ______.


Find the c.d.f. F(x) associated with the following p.d.f. f(x)

f(x) = `{{:(3(1 - 2x^2)",", 0 < x < 1),(0",", "otherwise"):}`

Find `P(1/4 < x < 1/3)` by using p.d.f. and c.d.f.


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