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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Fill in the blank : If x is continuous r.v. and F(xi) = P(X ≤ xi) = ∫-∞∞f(x)⋅dx then F(x) is called _______ - Mathematics and Statistics

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प्रश्न

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 _______

रिकाम्या जागा भरा

उत्तर

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

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Probability Distribution of a Continuous Random Variable
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Probability Distributions - Miscellaneous Exercise 8 [पृष्ठ १५४]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 8 Probability Distributions
Miscellaneous Exercise 8 | Q 2.07 | पृष्ठ १५४

संबंधित प्रश्‍न

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

 f(x) = sin x, for 0 ≤ x ≤ `π/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 0.10 0.15 0.20 0.25 0.15 0.1

Find the probability that

X is even


Check whether the following is a p.d.f. 

f(x) = `{(x, "for"  0 ≤ x ≤ 1),(2 - x, "for"  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 < 1.5),


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 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 more than 4 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(X > 0)


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(1 < 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).


State whether the following is True or False :

If X ~ B(n,p) and n = 6 and P(X = 4) = P(X = 2) then p = `(1)/(2)`


Solve the following problem :

In the following probability distribution of a r.v.X.

x 1 2 3 4 5
P (x) `(1)/(20)` `(3)/(20)` a 2a `(1)/(20)`

Find a and obtain the c.d.f. of X.


Solve the following problem :

Determine k if the p.d.f. of the r.v. is

f(x) = `{("ke"^(-thetax),  "for"  0 ≤ x < oo),(0, "otherwise".):}`
Find `"P"("X" > 1/theta)` and determine M is P(0 < X < M) = `(1)/(2)`


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


State whether the following statement is True or False:

The cumulative distribution function (c.d.f.) of a continuous random variable X is denoted by F and defined by

F(x) = `{:(0",",  "for all"  x ≤ "a"),( int_"a"^x  f(x) "d"x",",  "for all"  x ≥ "a"):}`


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