Advertisements
Advertisements
Question
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) = _______.
Options
`(1)/(9)`
`(2)/(9)`
`(3)/(9)`
`(4)/(9)`
Solution
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
RELATED QUESTIONS
Verify which of the following is p.d.f. of r.v. X:
f(x) = x, for 0 ≤ x ≤ 1 and 2 - x for 1 < x < 2
Verify which of the following is p.d.f. of r.v. X:
f(x) = 2, for 0 ≤ x ≤ 1.
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
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(0.5 ≤ X ≤ 1.5)
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(X > 0)
Following is the p. d. f. of a continuous r.v. X.
f(x) = `{(x/8, "for" 0 < x < 4),(0, "otherwise".):}`
Find F(x) at x = 0.5, 1.7 and 5.
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(X > 0)
If a r.v. X has p.d.f f(x) = `{("c"/x"," 1 < x < 3"," "c" > 0),(0"," "otherwise"):}`
Find c, E(X), and Var(X). Also Find F(x).
State whether the following is True or False :
If f(x) = k x (1 – x) for 0 < x < 1 = 0 otherwise k = 12
Solve the following problem :
In the following probability distribution of a r.v.X.
| x | 1 | 2 | 3 | 4 | 5 |
| P (x) | `(1)/(20)` | `(3)/(20)` | a | 2a | `(1)/(20)` |
Find a and obtain the c.d.f. of X.
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)
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(–1 < X < 1)
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)
Solve the following problem :
Let X denote the reaction temperature in Celsius of a certain chemical process. Let X have the p. d. f.
f(x) = `{((1)/(10), "for" -5 ≤ x < 5),(0, "otherwise".):}`
Compute P(X < 0).
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"):}`
Find the c.d.f. F(x) associated with the following p.d.f. f(x)
f(x) = `{{:(3(1 - 2x^2)",", 0 < x < 1),(0",", "otherwise"):}`
Find `P(1/4 < x < 1/3)` by using p.d.f. and c.d.f.
