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If F(x) is distribution function of discrete r.v.x with p.m.f. P(x) = x-13 for x = 0, 1 2, 3, and P(x) = 0 otherwise then F(4) = _______. - Mathematics and Statistics

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प्रश्न

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) = _______.

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उत्तर

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) = 1.

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Probability Distribution of Discrete Random Variables
  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 2.04 | पृष्ठ १५४

संबंधित प्रश्‍न

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

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


Choose the correct option from the given alternative:

If the 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) =


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)


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)


Find the probability distribution of number of heads in four tosses of a coin


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


Fill in the blank :

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


State whether the following is True or False :

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X 0 1 2 3 4 5
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Solve the following problem :

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

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Calculate E(X) and Var(X).


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

then k = ______


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

then Var(x) = ______


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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.


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