Advertisements
Advertisements
प्रश्न
The following is the p.d.f. of r.v. X :
f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise
P ( 1 < x < 2 )
उत्तर
P (1 < x < 2)
= ` int_(1)^2 f (x) dx`
= ` int_(1)^2 x/8 dx`
`1/8[x^2/2]_1^2`
=`1/8[4/2-1/2]`
=`3/16`
APPEARS IN
संबंधित प्रश्न
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) | 0.4 | 0.4 | 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 | 3 | 4 |
P(X) | 0.1 | 0.5 | 0.2 | − 0.1 | 0.2 |
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 |
Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the standard deviation of X.
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)
It is known that error in measurement of reaction temperature (in 0° c) in a certain experiment is continuous r.v. given by
f (x) = `x^2/3` , for –1 < x < 2 and = 0 otherwise
Find probability that X is negative
If the p.d.f. of c.r.v. X is f(x) = `x^2/18`, for -3 < x < 3 and = 0, otherwise, then P(|X| < 1) = ______.
Choose the correct option from the given alternative:
If p.m.f. of a d.r.v. X is P (X = x) = `((c_(x)^5 ))/2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise If a = P (X ≤ 2) and b = P (X ≥ 3), then E (X ) =
Solve the following :
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
The person on the high protein diet is interested gain of weight in a week.
The following is the c.d.f. of r.v. X
x | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
F(X) | 0.1 | 0.3 | 0.5 | 0.65 | 0.75 | 0.85 | 0.9 |
1 |
P (X ≤ 3/ X > 0)
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 the probability distribution of number of number of tails in three tosses of a coin
Find expected value and variance of X, the number on the uppermost face of a fair die.
Given that X ~ B(n, p), if n = 10 and p = 0.4, find E(X) 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) = _______
Choose the correct alternative :
If X ∼ B`(20, 1/10)` then E(X) = _______
Fill in the blank :
If X is discrete random variable takes the value x1, x2, x3,…, xn then \[\sum\limits_{i=1}^{n}\text{P}(x_i)\] = _______
Fill in the blank :
E(x) is considered to be _______ of the probability distribution of x.
State whether the following is True or False :
x | – 2 | – 1 | 0 | 1 | 2 |
P(X = x) | 0.2 | 0.3 | 0.15 | 0.25 | 0.1 |
If F(x) is c.d.f. of discrete r.v. X then F(–3) = 0
State whether the following is True or False :
If p.m.f. of discrete r.v. X is
x | 0 | 1 | 2 |
P(X = x) | q2 | 2pq | p2 |
then E(x) = 2p.
If r.v. X assumes values 1, 2, 3, ……. n with equal probabilities then E(X) = `("n" + 1)/(2)`
Solve the following problem :
The probability distribution of a discrete r.v. X is as follows.
X | 1 | 2 | 3 | 4 | 5 | 6 |
(X = x) | k | 2k | 3k | 4k | 5k | 6k |
Find P(X ≤ 4), P(2 < X < 4), P(X ≤ 3).
Solve the following problem :
Find the expected value and variance of the r. v. X if its probability distribution is as follows.
x | – 1 | 0 | 1 |
P(X = x) | `(1)/(5)` | `(2)/(5)` | `(2)/(5)` |
The p.m.f. of a d.r.v. X is P(X = x) = `{{:(((5),(x))/2^5",", "for" x = 0"," 1"," 2"," 3"," 4"," 5),(0",", "otherwise"):}` If a = P(X ≤ 2) and b = P(X ≥ 3), then
If the p.m.f. of a d.r.v. X is P(X = x) = `{{:(x/("n"("n" + 1))",", "for" x = 1"," 2"," 3"," .... "," "n"),(0",", "otherwise"):}`, then E(X) = ______
The probability distribution of X is as follows:
X | 0 | 1 | 2 | 3 | 4 |
P(X = x) | 0.1 | k | 2k | 2k | k |
Find k and P[X < 2]
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as number greater than 4 appears on at least one die.
Choose the correct alternative:
f(x) is c.d.f. of discete r.v. X whose distribution is
xi | – 2 | – 1 | 0 | 1 | 2 |
pi | 0.2 | 0.3 | 0.15 | 0.25 | 0.1 |
then F(– 3) = ______
The values of discrete r.v. are generally obtained by ______
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`
The probability distribution of X is as follows:
x | 0 | 1 | 2 | 3 | 4 |
P[X = x] | 0.1 | k | 2k | 2k | k |
Find
- k
- P[X < 2]
- P[X ≥ 3]
- P[1 ≤ X < 4]
- P(2)
Given below is the probability distribution of a discrete random variable x.
X | 1 | 2 | 3 | 4 | 5 | 6 |
P(X = x) | K | 0 | 2K | 5K | K | 3K |
Find K and hence find P(2 ≤ x ≤ 3)