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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 - Mathematics

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प्रश्न

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

पर्याय

  • i + 2n, i = 0, 1, 2 …, n

  • 2i – n, i = 0, 1, 2 …, n

  • n – i, i = 0, 1, 2 …, n

  • 2i + 2n, i = 0, 1, 2 …, n

MCQ
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उत्तर

2i – n, i = 0, 1, 2 …, n

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Random Variable
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Probability Distributions - Exercise 11.6 [पृष्ठ २१९]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 11 Probability Distributions
Exercise 11.6 | Q 6 | पृष्ठ २१९

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


In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images


A six sided die is marked ‘2’ on one face, ‘3’ on two of its faces, and ‘4’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images


Let X be a discrete random variable with the following p.m.f
`"P"(x) = {{:(0.3,  "for"  x = 3),(0.2,  "for"  x = 5),(0.3,  "for"  x = 8),(0.2,  "for"  x = 10),(0,  "otherwise"):}`
Find and plot the c.d.f. of X.


The discrete random variable X has the probability function

X 1 2 3 4
P(X = x) k 2k 3k 4k

Show that k = 0 1


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

Evaluate p(x < 6), p(x ≥ 6) and p(0 < x < 5)


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


Explain what are the types of random variable?


Define dicrete random Variable


Describe what is meant by a random variable


Explain the terms probability distribution function


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:

If c is a constant, then E(c) is


Choose the correct alternative: 

Which one is not an example of random experiment?


Choose the correct alternative: 

A variable which can assume finite or countably infinite number of values is known as


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(0 ≤ X ≤ 10)


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):}`
Is X a discrete random variable? Justify your answer


Consider a random variable X with p.d.f.
f(x) = `{(3x^2",",  "if"  0 < x < 1),(0",",  "otherwise"):}`
Find E(X) and V(3X – 2)


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