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Explain the terms probability distribution function - Business Mathematics and Statistics

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प्रश्न

Explain the terms probability distribution function

बेरीज

उत्तर

The probability distribution of a random variable X is defined only when we have the various values of the random variable e.g. x1, x2 …… xn together with respective probabilities p1, p2, p3 …… p4 satisfying

`sum_("i" = 1)^"n" "PI"` =1

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Random Variable
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Random Variable and Mathematical expectation - Exercise 6.1 [पृष्ठ १३३]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
पाठ 6 Random Variable and Mathematical expectation
Exercise 6.1 | Q 18. (iii) | पृष्ठ १३३

संबंधित प्रश्‍न

The distribution of a continuous random variable X in range (– 3, 3) is given by p.d.f.
f(x) = `{{:(1/16(3 + x)^2",", - 3 ≤ x ≤ - 1),(1/16(6 - 2x^2)",", - 1 ≤ x ≤ 1),(1/16(3 - x)^2",", 1 ≤ x ≤ 3):}`
Verify that the area under the curve is unity.


A continuous random variable X has the following distribution function
F(x) = `{{:(0",",  "if"  x ≤ 1),("k"(x - 1)^4",",  "if"  1 < x ≤ 3),(1",",  "if"  x > 3):}`
Find the Probability density function


Define random variable


State the properties of distribution function.


Choose the correct alternative: 

A discrete probability function p(x) is always


The probability function of a random variable X is given by
p(x) = `{{:(1/4",",  "for"  x = - 2),(1/4",",  "for"  x = 0),(1/2",",  "for"  x = 10),(0",",  "elsewhere"):}`
Evaluate the following probabilities
P(|X| ≤ 2)


Let X be a random variable with a cumulative distribution function.
F(x) = `{{:(0",",  "if"  x  < 0),(x/8",",  "if"  0 ≤ x ≤ 1),(1/4 + x/8",",  "if"  1 ≤ x ≤ 2),(3/4 + x/12",",  "if"  2 ≤ x < 3),(1",",  "for"  3 ≤ x):}`
Compute: (i) P(1 ≤ X ≤ 2) and (ii) P(X = 3)


The p.d.f. of X is defined as
f(x) = `{{:("k"",",  "for"  0 < x ≤ 4),(0",",  "otherwise"):}`
Find the value of k and also find P(2 ≤ X ≤ 4)


The probability distribution function of a discrete random variable X is
f(x) = `{{:(2k",",  x = 1),(3k",",  x = 3),(4k",", x = 5),(0",",  "otherwise"):}`
where k is some constant. Find P(X > 2) 


The probability density function of a continuous random variable X is
f(x) = `{{:("a" + "b"x^2",",  0 ≤ x ≤ 1),(0",",  "otherwise"):}`
where a and b are some constants. Find a and b if E(X) = `3/5`


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