Advertisements
Advertisements
प्रश्न
State whether the following is True or False :
If f(x) = k x (1 – x) for 0 < x < 1 = 0 otherwise k = 12
पर्याय
True
False
उत्तर
False
Since the function represents a p.d.f. 1
∴ `int_0^1 f(x)*dx` = 1
∴ `int_0^1 "k"x (1 - x)*dx` = 1
∴ `"k" int_0^1 (x - x^2)*dx` = 1
∴ `[x^2/2 - x^3/3]_0^1 = (1)/"k"`
∴ `(1)/(2) - (1)/(3) = (1)/"k"`
∴ `(1)/(6) = (1)/"k"`
∴ k = 6.
APPEARS IN
संबंधित प्रश्न
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
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) = 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)
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 < 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(1 < X < 2)
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).
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) = _______
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 :
The p.d.f. of the r.v. X is given by
f(x) = `{((1)/(2"a")",", "for" 0 < x= 2"a".),(0, "otherwise".):}`
Show that `"P"("X" < "a"/2) = "P"("X" > (3"a")/2)`
Solve the following problem :
Determine k if the p.d.f. of the r.v. is
f(x) = `{("ke"^(-thetax), "for" 0 ≤ x < oo),(0, "otherwise".):}`
Find `"P"("X" > 1/theta)` and determine M is P(0 < X < M) = `(1)/(2)`
The values of continuous r.v. are generally obtained by ______
State whether the following statement is True or False:
If f(x) = `{:("k"x (1 - x)",", "for" 0 < x < 1),(= 0",", "otherwise"):}`
is the p.d.f. of a r.v. X, then k = 12
If r.v. X assumes the values 1, 2, 3, …….., 9 with equal probabilities, then E(X) = 5
For the following probability density function of a random variable X, find P(|X| < 1).
`{:(f(x) = (x + 2)/18,";" "for" -2 < x < 4),( = 0,"," "otherwise"):}`
Find k, if the following function is p.d.f. of r.v.X:
f(x) = `{:(kx^2(1 - x)",", "for" 0 < x < 1),(0",", "otherwise"):}`
