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

Fill in the blank : If X is discrete random variable takes the value x1, x2, x3,…, xn then ∑i=1nP(xi) = _______ - Mathematics and Statistics

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प्रश्न

Fill in the blank :

If X is discrete random variable takes the value x1, x2, x3,…, xn then \[\sum\limits_{i=1}^{n}\text{P}(x_i)\] = _______

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उत्तर

If X is discrete random variable takes the value x1, x2, x3,…, xn then \[\sum\limits_{i=1}^{n}\text{P}(x_i)\] = 1.

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Probability Distribution of Discrete Random Variables
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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 2.03 | पृष्ठ १५४

संबंधित प्रश्‍न

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

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the standard deviation of X.


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

f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise.

Find P (x < 1·5)


If the p.d.f. of c.r.v. X is f(x) = `x^2/18`, for -3 < x < 3 and = 0, otherwise, then P(|X| < 1) = ______. 


Choose the correct option from the given alternative:

Find expected value of and variance of X for the following p.m.f.

X -2 -1 0 1 2
P(x) 0.3 0.3 0.1 0.05 0.25

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

Find p.m.f. of X.
i. P(–1 ≤ X ≤ 2)
ii. P(X ≤ 3 / X > 0).


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 ≥ 1.5)


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]`


Given that X ~ B(n,p), if n = 25, E(X) = 10, find p and Var (X).


Choose the correct alternative :

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


If r.v. X assumes values 1, 2, 3, ……. n with equal probabilities then E(X) = `("n" + 1)/(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)`

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) = ______


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


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