Advertisements
Advertisements
Question
Explain the terms probability Mass function
Solution
If X is a discrete random variable with distinct values x1, x2, …. xn, …, then the function, denoted by Px(x) and defined by
This is defined to be the probability mass function or discrete probability function of X.
APPEARS IN
RELATED QUESTIONS
Two balls are chosen randomly from an urn containing 6 red and 8 black balls. Suppose that we win ₹ 15 for each red ball selected and we lose ₹ 10 for each black ball selected. X denotes the winning amount, then find the values of X and number of points in its inverse images
The discrete random variable X has the probability function
X | 1 | 2 | 3 | 4 |
P(X = x) | k | 2k | 3k | 4k |
Show that k = 0 1
A continuous random variable X has the following distribution function
F(x) = `{{:(0",", "if" x ≤ 1),("k"(x - 1)^4",", "if" 1 < x ≤ 3),(1",", "if" x > 3):}`
Find the Probability density function
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
What are the properties of continuous random variable?
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(X ≤ 0)
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(X < 0)
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)
The probability density function of a continuous random variable X is
f(x) = `{{:("a" + "b"x^2",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
where a and b are some constants. Find a and b if E(X) = `3/5`