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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

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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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  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

Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images


Choose the correct alternative:

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are


The discrete random variable X has the following probability function.
P(X = x) = `{{:("k"x,  x = 2","  4","  6),("k"(x - 2),  x = 8),(0,  "otherwise"):}`
where k is a constant. Show that k = `1/18`


The discrete random variable X has the probability function.

Value
of X = x
0 1 2 3 4 5 6 7
P(x) 0 k 2k 2k 3k k2 2k2 7k2 + k

If P(X ≤ x) > `1/2`, then find the minimum value of x.


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


The length of time (in minutes) that a certain person speaks on the telephone is found to be random phenomenon, with a probability function specified by the probability density function f(x) as 
f(x) = `{{:("Ae"^((-x)/5)",",  "for"  x ≥ 0),(0",",  "otherwise"):}`
What is the probability that the number of minutes that person will talk over the phone is (i) more than 10 minutes, (ii) less than 5 minutes and (iii) between 5 and 10 minutes


What are the properties of continuous random variable?


Choose the correct alternative:

A variable that can assume any possible value between two points is called


Choose the correct alternative: 

The height of persons in a country is a random variable of the type


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 ≤ 0)


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