Advertisements
Advertisements
प्रश्न
Explain the distribution function of a random variable
Advertisements
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
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 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`
Distinguish between discrete and continuous random variables.
Explain the terms probability density function
State the properties of distribution function.
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)
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 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)
