Advertisements
Advertisements
प्रश्न
Choose the correct alternative :
Given p.d.f. of a continuous r.v.X as f(x) = `x^2/(3)` for –1 < x < 2 = 0 otherwise then F(1) = _______.
पर्याय
`(1)/(9)`
`(2)/(9)`
`(3)/(9)`
`(4)/(9)`
उत्तर
F(1) = P(X ≤ 1)
= `int_(-1)^(1) x^2/(3)*dx`
= `(1)/(3) int_(-1)^(1) x^2*dx`
= `(1)/(9)[x^3]_(-1)^(1)`
= `(2)/(9)`.
APPEARS IN
संबंधित प्रश्न
Verify which of the following is p.d.f. of r.v. X:
f(x) = sin x, for 0 ≤ x ≤ `π/2`
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 | 0.10 | 0.15 | 0.20 | 0.25 | 0.15 | 0.1 |
Find the probability that
X is non-negative
Check whether the following is a p.d.f.
f(x) = `{(x, "for" 0 ≤ x ≤ 1),(2 - x, "for" 1 < x ≤ 2.):}`
Check whether the following is a p.d.f.
f(x) = 2 for 0 < x < q.
The following is the p.d.f. of a r.v. X.
f(x) = `{(x/(8), "for" 0 < x < 4),(0, "otherwise."):}`
Find P(X > 2)
Let X be the amount of time for which a book is taken out of library by a randomly selected student and suppose that X has p.d.f.
f(x) = `{(0.5x, "for" 0 ≤ x ≤ 2),(0, "otherwise".):}`
Calculate : P(X ≤ 1)
Suppose X is the waiting time (in minutes) for a bus and its p. d. f. is given by
f(x) = `{(1/5, "for" 0 ≤ x ≤ 5),(0, "otherwise"):}`
Find the probability that waiting time is between 1 and 3 minutes.
Suppose X is the waiting time (in minutes) for a bus and its p. d. f. is given by
f(x) = `{(1/5, "for" 0 ≤ x ≤ 5),(0, "otherwise".):}`
Find the probability that waiting time is more than 4 minutes.
Suppose error involved in making a certain measurement is a continuous r. v. X with p.d.f.
f(x) = `{("k"(4 - x^2), "for" -2 ≤ x ≤ 2),(0, "otherwise".):}`
compute P(–1 < X < 1)
The p.d.f. of a continuous r.v. X is
f(x) = `{((3x^2)/(8), 0 < x < 2),(0, "otherwise".):}`
Determine the c.d.f. of X and hence find P(X < –2)
The p.d.f. of a continuous r.v. X is
f(x) = `{((3x^2)/(8), 0 < x < 2),(0, "otherwise".):}`
Determine the c.d.f. of X and hence find P(1 < X < 2)
Choose the correct alternative :
If p.m.f. of r.v.X is given below.
| x | 0 | 1 | 2 |
| P(x) | q2 | 2pq | p2 |
Then Var(X) = _______
State whether the following is True or False :
If f(x) = k x (1 – x) for 0 < x < 1 = 0 otherwise k = 12
State whether the following is True or False :
If X ~ B(n,p) and n = 6 and P(X = 4) = P(X = 2) then p = `(1)/(2)`
Solve the following problem :
Suppose error involved in making a certain measurement is a continuous r.v.X with p.d.f.
f(x) = `{("k"(4 - x^2), "for" -2 ≤ x ≤ 2),(0, "otherwise".):}`
Compute P(X < – 0.5 or X > 0.5)
If r.v. X assumes the values 1, 2, 3, …….., 9 with equal probabilities, then E(X) = 5
State whether the following statement is True or False:
The cumulative distribution function (c.d.f.) of a continuous random variable X is denoted by F and defined by
F(x) = `{:(0",", "for all" x ≤ "a"),( int_"a"^x f(x) "d"x",", "for all" x ≥ "a"):}`
