Advertisements
Advertisements
प्रश्न
What are the properties of discrete random variable
Advertisements
उत्तर
The probability mass function p(x) must satisfy the following conditions
(i) p(xi) ≥ 0 ∀ i
(ii) `sum_("i" = 1)^oo "p"(x_"i")` = 1
APPEARS IN
संबंधित प्रश्न
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
The discrete random variable X has the probability function.
| Value of X = x |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Evaluate p(x < 6), p(x ≥ 6) and p(0 < x < 5)
The distribution of a continuous random variable X in range (– 3, 3) is given by p.d.f.
f(x) = `{{:(1/16(3 + x)^2",", - 3 ≤ x ≤ - 1),(1/16(6 - 2x^2)",", - 1 ≤ x ≤ 1),(1/16(3 - x)^2",", 1 ≤ x ≤ 3):}`
Verify that the area under the curve is unity.
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
Define dicrete random Variable
Explain the distribution function of a random variable
Choose the correct alternative:
A formula or equation used to represent the probability distribution of a continuous random variable is called
Choose the correct alternative:
If c is a constant, then E(c) is
Choose the correct alternative:
A set of numerical values assigned to a sample space is called
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| ≤ 2)
