Advertisements
Advertisements
Question
Fill in the blank :
If X is discrete random variable takes the value x1, x2, x3,…, xn then \[\sum\limits_{i=1}^{n}\text{P}(x_i)\] = _______
Solution
If X is discrete random variable takes the value x1, x2, x3,…, xn then \[\sum\limits_{i=1}^{n}\text{P}(x_i)\] = 1.
APPEARS IN
RELATED QUESTIONS
State if the following is not the probability mass function of a random variable. Give reasons for your answer.
Y | −1 | 0 | 1 |
P(Y) | 0.6 | 0.1 | 0.2 |
State if the following is not the probability mass function of a random variable. Give reasons for your answer.
X | 0 | -1 | -2 |
P(X) | 0.3 | 0.4 | 0.3 |
Find expected value and variance of X for the following p.m.f.
x | -2 | -1 | 0 | 1 | 2 |
P(X) | 0.2 | 0.3 | 0.1 | 0.15 | 0.25 |
The following is the p.d.f. of r.v. X:
f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise.
Find P (x < 1·5)
The following is the p.d.f. of r.v. X:
f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise.
P(x > 2)
Suppose that X is waiting time in minutes for a bus and its p.d.f. is given by f(x) = `1/5`, for 0 ≤ x ≤ 5 and = 0 otherwise.
Find the probability that the waiting time is more than 4 minutes.
Solve the following :
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
Amount of syrup prescribed by physician.
Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f
f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise. Calculate: P(x ≥ 1.5)
Find k if the following function represents the p. d. f. of a r. v. X.
f(x) = `{(kx, "for" 0 < x < 2),(0, "otherwise."):}`
Also find `"P"[1/4 < "X" < 1/2]`
Given that X ~ B(n,p), if n = 25, E(X) = 10, find p and Var (X).
Choose the correct alternative :
X: is number obtained on upper most face when a fair die….thrown then E(X) = _______.
X is r.v. with p.d.f. f(x) = `"k"/sqrt(x)`, 0 < x < 4 = 0 otherwise then x E(X) = _______
If r.v. X assumes values 1, 2, 3, ……. n with equal probabilities then E(X) = `("n" + 1)/(2)`
Solve the following problem :
The p.m.f. of a r.v.X is given by
`P(X = x) = {(((5),(x)) 1/2^5", ", x = 0", "1", "2", "3", "4", "5.),(0,"otherwise"):}`
Show that P(X ≤ 2) = P(X ≤ 3).
If X denotes the number on the uppermost face of cubic die when it is tossed, then E(X) is ______
Find mean for the following probability distribution.
X | 0 | 1 | 2 | 3 |
P(X = x) | `1/6` | `1/3` | `1/3` | `1/6` |
The probability distribution of a discrete r.v.X is as follows.
x | 1 | 2 | 3 | 4 | 5 | 6 |
P(X = x) | k | 2k | 3k | 4k | 5k | 6k |
Complete the following activity.
Solution: Since `sum"p"_"i"` = 1
k = `square`
The probability distribution of a discrete r.v.X is as follows.
x | 1 | 2 | 3 | 4 | 5 | 6 |
P(X = x) | k | 2k | 3k | 4k | 5k | 6k |
Complete the following activity.
Solution: Since `sum"p"_"i"` = 1
P(X ≤ 4) = `square + square + square + square = square`