Advertisements
Advertisements
प्रश्न
Explain the distribution function of a random variable
उत्तर
The discrete cumulative distribution function or distribution function of a real-valued discrete random variable X takes the countable number of points x1, x2, …. with corresponding probabilities p(x1), p(x2),… and then the cumulative distribution function is defined by
Fx(x) = P(X ≤ x), for all x ∈ R
i.e. Fx (x) = `sum_(x ≤ x) "P"(x_"i")`
APPEARS IN
संबंधित प्रश्न
The discrete random variable X has the following probability function.
P(X = x) = `{{:("k"x, x = 2"," 4"," 6),("k"(x - 2), x = 8),(0, "otherwise"):}`
where k is a constant. Show that k = `1/18`
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
Explain the terms probability Mass function
What are the properties of discrete random variable
State the properties of distribution function.
Choose the correct alternative:
A variable which can assume finite or countably infinite number of values is known as
Choose the correct alternative:
A discrete probability function p(x) is always
Choose the correct alternative:
The probability density function p(x) cannot exceed
Choose the correct alternative:
The height of persons in a country is a random variable of the type
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)