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| ≤ 2)
Advertisements
उत्तर
| X | – 2 | 0 | 10 |
| P(X = x) | `1/4` | `1/4` | `1/2` |
P(|x| ≤ 2) = P(– 2 ≤ X ≤ 2)
= P(X = – 2) + P(X = 0)
= `1/4 + 1/4`
= `2/4`
= `1/2`
APPEARS IN
संबंधित प्रश्न
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 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.
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 k
Define random variable
Explain the terms probability distribution function
State the properties of distribution function.
Choose the correct alternative:
If the random variable takes negative values, then the negative values will have
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)
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 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)
