Advertisements
Advertisements
Question
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) = ______
Options
0
1
0.2
0.15
Solution
0
RELATED QUESTIONS
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 |
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)
Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the standard deviation of X.
The following is the p.d.f. of r.v. X:
f(x) = `x/8`, for 0 < x < 4 and = 0 otherwise.
P(x > 2)
Choose the correct option from the given alternative:
If a d.r.v. X takes values 0, 1, 2, 3, . . . which probability P (X = x) = k (x + 1)·5 −x , where k is a constant, then P (X = 0) =
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 |
Solve the following :
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
The person on the high protein diet is interested gain of weight in a week.
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.
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).
Find k if the following function represents the p. d. f. of a r. v. X.
f(x) = `{(kx, "for" 0 < x < 2),(0, "otherwise."):}`
Also find `"P"[1/4 < "X" < 1/2]`
Given that X ~ B(n,p), if n = 10, E(X) = 8, find Var(X).
The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.
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) = _______
Solve the following problem :
The probability distribution of a discrete r.v. X is as follows.
X | 1 | 2 | 3 | 4 | 5 | 6 |
(X = x) | k | 2k | 3k | 4k | 5k | 6k |
Determine the value of k.
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 | ... | n |
P(X = x) | `(1)/"n"` | `(1)/"n"` | `(1)/"n"` | ... | `(1)/"n"` |
Solve the following problem :
Let X∼B(n,p) If n = 10 and E(X)= 5, find p and Var(X).
If a d.r.v. X takes values 0, 1, 2, 3, … with probability P(X = x) = k(x + 1) × 5–x, where k is a constant, then P(X = 0) = ______
If the p.m.f. of a d.r.v. X is P(X = x) = `{{:(x/("n"("n" + 1))",", "for" x = 1"," 2"," 3"," .... "," "n"),(0",", "otherwise"):}`, then E(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) = ______
E(x) is considered to be ______ of the probability distribution of x.
The p.m.f. of a random variable X is as follows:
P (X = 0) = 5k2, P(X = 1) = 1 – 4k, P(X = 2) = 1 – 2k and P(X = x) = 0 for any other value of X. Find k.
Given below is the probability distribution of a discrete random variable x.
X | 1 | 2 | 3 | 4 | 5 | 6 |
P(X = x) | K | 0 | 2K | 5K | K | 3K |
Find K and hence find P(2 ≤ x ≤ 3)