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Choose the correct alternative: If aotherwisef(x)={2x0≤x≤a0otherwise is a probability density function of a random variable, then the value of a is - Mathematics

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प्रश्न

Choose the correct alternative:

If `f(x) = {{:(2x, 0 ≤ x ≤ "a"),(0, "otherwise"):}` is a probability density function of a random variable, then the value of a is

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MCQ
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उत्तर

1

shaalaa.com
Continuous Distributions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 11: Probability Distributions - Exercise 11.6 [पृष्ठ २२०]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 11 Probability Distributions
Exercise 11.6 | Q 16 | पृष्ठ २२०

संबंधित प्रश्‍न

The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(1.2 ≤ X < 1.8)


The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(0.5 ≤ X < 1.5)


Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
`f(x) = {{:(k, 200 ≤ x ≤ 600),(0, "otherwise"):}`
Find the value of k


Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
`f(x) = {{:(k, 200 ≤ x ≤ 600),(0, "otherwise"):}`
Find the distribution function


Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
`f(x) = {{:(k, 200 ≤ x ≤ 600),(0, "otherwise"):}`
Find the probability that daily sales will fall between 300 litres and 500 litres?


The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find the value of k 


The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(X < 3)


The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(5 ≤ X)


The probability density function of X is given by
`f(x) = {(k"e"^(- x/3), "for"  x > 0),(0,"for"  x ≤ 0):}`
Find P(X ≤ 4)


If X is the random variable with probability density function f(x) given by,
`f(x) = {{:(x + 1",", -1 ≤ x < 0),(-x +1",",   0 ≤ x < 1),(0, "otherwise"):}`
then find the distribution function F(x)


If X is the random variable with distribution function F(x) given by,
F(x) = `{{:(0",", - oo < x < 0),(1/2(x^2 + x)",", 0 ≤ x ≤ 1),(1",", 1 ≤ x < oo):}`
then find the probability density function f(x)


Choose the correct alternative:

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is 
`f(x) = {{:(1/l, 0 < x < l),(0, l ≤ x < 2l):}`
The mean and variance of the shorter of the two pieces are respectively


Choose the correct alternative:

If the function f(x) = `1/12` for a < x < b, represents a probability density function of a continuous random variable X, then which of the following cannot be the value of a and b?


Choose the correct alternative:

The random variable X has the probability density function
`f(x) = {{:("a"x + "b", 0 < x < 1),(0, "otherwise"):}`
and E(X) = `7/12`, then a and b are respectively


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