Advertisements
Advertisements
प्रश्न
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)
उत्तर
X | – 2 | 0 | 10 |
PX = x) | `1/4` | `1/4` | `1/2` |
P(x ≤ 0) = P( x = – 2) + P(x = 0)
= `1/4+ 1/4`
= `2/4`
= `1/2`
APPEARS IN
संबंधित प्रश्न
In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images
Construct cumulative distribution function for the given probability distribution.
X | 0 | 1 | 2 | 3 |
P(X = x) | 0.3 | 0. | 0.4 | 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)
Suppose that the time in minutes that a person has to wait at a certain station for a train is found to be a random phenomenon with a probability function specified by the distribution function
F(x) = `{{:(0",", "for" x ≤ 0),(x/2",", "for" 0 ≤ x < 1),(1/2",", "for" ≤ x < 2),(x/4",", "for" 2 ≤ x < 4),(1",", "for" x ≥ 4):}`
Is the distribution function continuous? If so, give its probability density function?
Choose the correct alternative:
If c is a constant, then E(c) is
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
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):}`
Is X a discrete random variable? Justify your answer
The p.d.f. of X is defined as
f(x) = `{{:("k"",", "for" 0 < x ≤ 4),(0",", "otherwise"):}`
Find the value of k and also find P(2 ≤ X ≤ 4)
Consider a random variable X with p.d.f.
f(x) = `{(3x^2",", "if" 0 < x < 1),(0",", "otherwise"):}`
Find E(X) and V(3X – 2)