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प्रश्न
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"):}`
विकल्प
True
False
उत्तर
True
संबंधित प्रश्न
The time (in minutes) for a lab assistant to prepare the equipment for a certain experiment is a random variable taking values between 25 and 35 minutes with p.d.f
`f(x) = {{:(1/10",", 25 ≤ x ≤ 35),(0",", "otherwise"):}`
What is the probability that preparation time exceeds 33 minutes? Also, find the c.d.f. of X.
Verify which of the following is p.d.f. of r.v. X:
f(x) = sin x, for 0 ≤ x ≤ `π/2`
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.
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
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 odd
Check whether the following is a p.d.f.
f(x) = `{(x, "for" 0 ≤ x ≤ 1),(2 - x, "for" 1 < 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(X > 0)
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)
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)
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.
Fill in the blank :
If x is continuous r.v. and F(xi) = P(X ≤ xi) = `int_(-oo)^(oo) f(x)*dx` then F(x) is called _______
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 :
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(X < – 0.5 or X > 0.5)
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)`
Solve the following problem :
The p.d.f. of the r.v. X is given by
f(x) = `{("k"/sqrt(x), "for" 0 < x < 4.),(0, "otherwise".):}`
Determine k, the c.d.f. of X, and hence find P(X ≤ 2) and P(X ≥ 1).
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:
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
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"):}`
