Advertisements
Advertisements
प्रश्न
Choose the correct option from the given alternative:
Find expected value of and variance of X for the following p.m.f.
X | -2 | -1 | 0 | 1 | 2 |
P(x) | 0.3 | 0.3 | 0.1 | 0.05 | 0.25 |
विकल्प
0·85
– 0·35
0·15
– 0·15
उत्तर
Explanation:
E(x) = ∑xipi
E(x) = (-2)(0.3) + (-1)(0.3) + (0)(0.1) + (1)(0.05) + (2)(0.25)
= -0.6 - 0.3 + 0 + 0.05 + 0.5
= -0.35
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 |
A random variable X has the following probability distribution:
X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Determine:
- k
- P(X < 3)
- P( X > 4)
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.
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 waiting time is between 1 and 3.
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 ) =
Choose the correct option from the given alternative:
If the a d.r.v. X has the following probability distribution :
x | -2 | -1 | 0 | 1 | 2 | 3 |
p(X=x) | 0.1 | k | 0.2 | 2k | 0.3 | k |
then P (X = −1) =
Solve the following :
The following probability distribution of r.v. X
X=x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
P(X=x) | 0.05 | 0.1 | 0.15 | 0.20 | 0.25 | 0.15 | 0.1 |
Find the probability that
X is positive
Solve the following problem :
A fair coin is tossed 4 times. Let X denote the number of heads obtained. Identify the probability distribution of X and state the formula for p. m. f. of X.
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 |
Find p.m.f. of X.
i. P(–1 ≤ X ≤ 2)
ii. P(X ≤ 3 / X > 0).
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 (–1 ≤ X ≤ 2)
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)
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(0.5 ≤ x ≤ 1.5)
Find the probability distribution of number of number of tails in three tosses of a coin
70% of the members favour and 30% oppose a proposal in a meeting. The random variable X takes the value 0 if a member opposes the proposal and the value 1 if a member is in favour. Find E(X) and Var(X).
Choose the correct alternative :
If X ∼ B`(20, 1/10)` then E(X) = _______
If F(x) is distribution function of discrete r.v.X with p.m.f. P(x) = `k^4C_x` for x = 0, 1, 2, 3, 4 and P(x) = 0 otherwise then F(–1) = _______
State whether the following is True or False :
If P(X = x) = `"k"[(4),(x)]` for x = 0, 1, 2, 3, 4 , then F(5) = `(1)/(4)` when F(x) is c.d.f.
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.
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).
Solve the following problem :
Find the expected value and variance of the r. v. X if its probability distribution is as follows.
x | 1 | 2 | 3 |
P(X = x) | `(1)/(5)` | `(2)/(5)` | `(2)/(5)` |
Solve the following problem :
Let X∼B(n,p) If n = 10 and E(X)= 5, find p and Var(X).
If the p.m.f. of a d.r.v. X is P(X = x) = `{{:(("c")/x^3",", "for" x = 1"," 2"," 3","),(0",", "otherwise"):}` then E(X) = ______
If a d.r.v. X has the following probability distribution:
X | –2 | –1 | 0 | 1 | 2 | 3 |
P(X = x) | 0.1 | k | 0.2 | 2k | 0.3 | k |
then P(X = –1) is ______
If a d.r.v. X has the following probability distribution:
X | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X = x) | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
then k = ______
Find mean for the following probability distribution.
X | 0 | 1 | 2 | 3 |
P(X = x) | `1/6` | `1/3` | `1/3` | `1/6` |
Find the expected value and variance of r.v. X whose p.m.f. is given below.
X | 1 | 2 | 3 |
P(X = x) | `1/5` | `2/5` | `2/5` |
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) = ______
If p.m.f. of r.v. X is given below.
x | 0 | 1 | 2 |
P(x) | q2 | 2pq | p2 |
then Var(x) = ______
The values of discrete r.v. are generally obtained by ______