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Choose the correct alternative: A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the

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प्रश्न

Choose the correct alternative:

A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

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

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 11 Probability Distributions
Exercise 11.6 | Q 4 | पृष्ठ २१९

संबंधित प्रश्‍न

Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.

f (x) = k `(4 – x^2 )`, for –2 ≤ x ≤ 2 and = 0 otherwise.

P(x > 0)


The following is the p.d.f. of continuous r.v.

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

Find F(x) at x = 0·5 , 1.7 and 5


Solve the following problem :

A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of winning amount.


It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64),  "for"  0 ≤ x ≤ 4),(0,   "otherwise."):}`
Verify whether f(x) is a p.d.f.


It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.

f(x) = `{(x^3/(64),  "for"  0 ≤ x ≤ 4),(0,   "otherwise."):}`
Find P(0 < X ≤ 1).


Solve the following problem :

Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.

A highway safety group is interested in the speed (km/hrs) of a car at a check point.


Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is ______.


A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the cumulative distribution function


A random variable X has the following probability mass function.

x 1 2 3 4 5
F(x) k2 2k2 3k2 2k 3k

Find P(2 ≤ X < 5)


The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0,  "for" - oo < x < 0),(1/2,  "for"  0 ≤ x < 1),(3/5,  "for"  1 ≤ x < 2),(4/5,  "for"  2 ≤ x < 4),(9/5,  "for"  3 ≤ x < 4),(1,  "for"   ≤ x < oo):}`
Find P(X ≥ 2)


The p.m.f. of a random variable X is

P(x) = `(5 - x)/10`,   x = 1, 2, 3, 4
       = 0,            otherwise

The value of E(X) is ______ 


For a random variable X, if Var (X) = 5 and E (X2) = 21, the value of E (X) is ______


A card is chosen from a well-shuffled pack of cards. The probability of getting an ace of spade or a jack of diamond is ______.


Two coins are tossed. Then the probability distribution of number of tails is.


The c.d.f. of a discrete r.v. X is

X = x -4 -2 -1 0 2 4 6 8
F(x) 0.2 0.4 0.55 0.6 0.75 0.80 0.95 1

Then P(X ≤ 4|X > -1) = ?


Two cards are randomly drawn, with replacement. from a well shuffled deck of 52 playing cards. Find the probability distribution of the number of aces drawn.


For the following distribution function F(x) of a rv.x.

x 1 2 3 4 5 6
F(x) 0.2 0.37 0.48 0.62 0.85 1

P(3 < x < 5) =


If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.


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