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प्रश्न
Choose the correct alternative:
The probability density function p(x) cannot exceed
विकल्प
zero
one
mean
infinity
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उत्तर
one
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संबंधित 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
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"):}`
Find the value of A that makes f(x) a p.d.f.
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
Distinguish between discrete and continuous random variables.
Choose the correct alternative:
If c is a constant in a continuous probability distribution, then p(x = c) is always equal to
Choose the correct alternative:
Which one is not an example of random experiment?
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):}`
Compute: (i) P(1 ≤ X ≤ 2) and (ii) P(X = 3)
The probability distribution function of a discrete random variable X is
f(x) = `{{:(2k",", x = 1),(3k",", x = 3),(4k",", x = 5),(0",", "otherwise"):}`
where k is some constant. Find k
The probability density function of a continuous random variable X is
f(x) = `{{:(a + bx^2",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
where a and b are some constants. Find Var(X)
