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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 - Mathematics

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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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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

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

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

Find expression for c.d.f. of X


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


Given the p.d.f. of a continuous r.v. X ,

f (x) = `x^2/3` , for –1 < x < 2 and = 0 otherwise

Determine c.d.f. of X hence find P(1 < x < 2)


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.


Fill in the blank :

The values of discrete r.v. are generally obtained by _______


c.d.f. of a discrete random variable X is


A random variable X has the following probability distribution:

X = x 0 1 2 3
P (X = x) `1/10` `1/2` `1/5` k

Then the value of k is


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 ______.


Find the probability mass function and cumulative distribution function of a number of girl children in families with 4 children, assuming equal probabilities for boys and girls


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 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 P(X ≥ 1)


The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0,  - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`
Find P(X ≥ 2)


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)


Choose the correct alternative:

Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day.
II. The number of customers in a queue to buy train tickets at a moment.
III. The time taken to complete a telephone call.


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


A random variable X has the following probability distribution:

X 1 2 3 4
P(X) `1/3` `2/9` `1/3` `1/9`

1hen, the mean of this distribution 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

The probability distribution of a random variable X is given below.

X = k 0 1 2 3 4
P(X = k) 0.1 0.4 0.3 0.2 0

The variance of X is ______


The p.d.f. of a continuous random variable X is

f(x) = 0.1 x, 0 < x < 5

= 0, otherwise

Then the value of P(X > 3) is ______ 


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 ______.


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