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
An urn contains 5 mangoes and 4 apples. Three fruits are taken at random. If the number of apples taken is a random variable, then 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`
Define random variable
Distinguish between discrete and continuous random variables.
State the properties of distribution function.
Choose the correct alternative:
A variable that can assume any possible value between two points is called
Choose the correct alternative:
If c is a constant, then E(c) is
Choose the correct alternative:
If c is a constant in a continuous probability distribution, then p(x = c) is always equal to
The probability distribution function of a discrete random variable X is
f(x) = `{{:(2k",", x = 1),(3k",", x = 3),(4k",", x = 5),(0",", "otherwise"):}`
where k is some constant. Find P(X > 2)
