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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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उत्तर

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 11: Probability Distributions - Exercise 11.6 [पृष्ठ २१९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 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 (–0·5 < x or x > 0·5)


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 :

Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.

An economist is interested the number of unemployed graduate in the town of population 1 lakh.


In the p.m.f. of r.v. X

X 1 2 3 4 5
P (X) `1/20` `3/20` a 2a `1/20`

Find a and obtain c.d.f. of X. 


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.


Solve the following problem :

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

An economist is interested in knowing the number of unemployed graduates in the town with a population of 1 lakh.


Three fair coins are tossed simultaneously. Find the probability mass function for a number of heads that occurred


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


Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by 
`f(x) = {{:((x^2 + 1)/k","  "for"  x = 0","  1","  2),(0","  "otherwise"):}` 
Find the value of k


Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by 
`f(x) = {{:((x^2 + 1)/k","  "for"  x = 0","  1","  2),(0","  "otherwise"):}` 
Find P(X ≥ 1)


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 the probability mass function


If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by

X = x - 1.5 -0.5 0.5 1.5 2.5
P(X = x) 0.05 0.2 0.15 0.25 0.35

then, F(1.5) - F(- 0.5) = ?


Choose the correct alternative:

Suppose that X takes on one of the values 0, 1 and 2. If for some constant k, P(X = i) = kP(X = i – 1) for i = 1, 2 and P(X = 0) = `1/7`. Then the value of k is


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 ______ 


If the probability function of a random variable X is defined by P(X = k) = a`((k + 1)/2^k)` for k - 0, 1, 2, 3, 4, 5, then the probability that X takes a prime value is ______


The probability distribution of a random variable X is given below. If its mean is 4.2, then the values of a and bar respectively 

X = x 1 2 3 4 5 6
P(X = x) a a a b b 0.3

At random variable X – B(n, p), if values of mean and variance of X are 18 and 12 respectively, then total number of possible values of X are ______.


Find the probability of getting the sum as a perfect square number when two dice are thrown together.


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