Advertisements
Advertisements
प्रश्न
Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by
`f(x) = {{:((x^2 + 1)/k"," "for" x = 0"," 1"," 2),(0"," "otherwise"):}`
Find P(X ≥ 1)
उत्तर
P(X ≥ 1) = = P(X = 1) + P(X = 2)
= `2/8 + 5/8 + 7/8`
APPEARS IN
संबंधित प्रश्न
Choose the correct option from the given alternative:
If the a d.r.v. X has the following probability distribution:
X | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X=x) | k | 2k | 2k | 3k | k2 | 2k2 | 7k2+k |
k =
The p.m.f. of a r.v. X is given by P (X = x) =`("" ^5 C_x ) /2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise.
Then show that P (X ≤ 2) = P (X ≥ 3).
In the p.m.f. of r.v. X
X | 1 | 2 | 3 | 4 | 5 |
P (X) | `1/20` | `3/20` | a | 2a | `1/20` |
Find a and obtain c.d.f. of X.
Fill in the blank :
The value of continuous r.v. are generally obtained by _______
Solve the following problem :
Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.
Amount of syrup prescribed by a physician.
Solve the following problem :
Identify the random variable as discrete or continuous in each of the following. Identify its range if it is discrete.
Twelve of 20 white rats available for an experiment are male. A scientist randomly selects 5 rats and counts the number of female rats among them.
A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the probability mass function
A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find P(X ≥ 6)
Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by
`f(x) = {{:((x^2 + 1)/k"," "for" x = 0"," 1"," 2),(0"," "otherwise"):}`
Find the value of k
Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by
`f(x) = {{:((x^2 + 1)/k"," "for" x = 0"," 1"," 2),(0"," "otherwise"):}`
Find cumulative distribution function
The cumulative distribution function of a discrete random variable is given by
F(x) = `{{:(0, - oo < x < - 1),(0.15, - 1 ≤ x < 0),(0.35, 0 ≤ x < 1),(0.60, 1 ≤ x < 2),(0.85, 2 ≤ x < 3),(1, 3 ≤ x < oo):}`
Find P(X ≥ 2)
A random variable X has the following probability mass function.
x | 1 | 2 | 3 | 4 | 5 |
F(x) | k2 | 2k2 | 3k2 | 2k | 3k |
Find the value of k
If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by
X = x | - 1.5 | -0.5 | 0.5 | 1.5 | 2.5 |
P(X = x) | 0.05 | 0.2 | 0.15 | 0.25 | 0.35 |
then, F(1.5) - F(- 0.5) = ?
Choose the correct alternative:
Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with Probability 0.5. Assume that the results of the flips are independent and let X equal the total number of heads that result. The value of E[X] is
If A = {x ∈ R : x2 - 5 |x| + 6 = 0}, then n(A) = _____.
A random variable X has the following probability distribution:
X | 1 | 2 | 3 | 4 |
P(X) | `1/3` | `2/9` | `1/3` | `1/9` |
1hen, the mean of this distribution is ______
The c.d.f. of a discrete r.v. x is
x | 0 | 1 | 2 | 3 | 4 | 5 |
F(x) | 0.16 | 0.41 | 0.56 | 0.70 | 0.91 | 1.00 |
Then P(1 < x ≤ 4) = ______
A random variable X has the following probability distribution:
X = xi | 1 | 2 | 3 | 4 |
P(X = xi) | 0.2 | 0.15 | 0.3 | 0.35 |
The mean and the variance are respectively ______.
If f(x) = `k/2^x` is a probability distribution of a random variable X that can take on the values x = 0, 1, 2, 3, 4. Then, k is equal to ______.