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 the value of k
Advertisements
उत्तर
Given f is a probability mass function
`sum_x "f"(x)` = 1
Probability mass function is
| x | 0 | 1 | 2 |
| F(x) | `1/k` | `2/k` | `5/k` |
`1/k + 2/k + 5/k` = 1
`8/k` = 1
k = 8
APPEARS IN
संबंधित प्रश्न
Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f.
f (x) = k `(4 – x^2 )`, for –2 ≤ x ≤ 2 and = 0 otherwise.
P(x > 0)
Given the p.d.f. of a continuous r.v. X ,
f (x) = `x^2/ 3` , for –1 < x < 2 and = 0 otherwise
Determine c.d.f. of X hence find P( X > 0)
Solve the following problem :
A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of winning amount.
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.
An economist is interested in knowing the number of unemployed graduates in the town with a population of 1 lakh.
The probability distribution of a r.v. X is
| X = x | -3 | -2 | -1 | 0 | 1 |
| P(X = x) | 0.3 | 0.2 | 0.25 | 0.1 | 0.15 |
Then F (-1) = ?
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(4 ≤ X < 10)
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, "for" - oo < x < 0),(1/2, "for" 0 ≤ x < 1),(3/5, "for" 1 ≤ x < 2),(4/5, "for" 2 ≤ x < 4),(9/5, "for" 3 ≤ x < 4),(1, "for" ≤ x < oo):}`
Find P(X ≥ 2)
For a random variable X, if Var (X) = 5 and E (X2) = 21, the value of E (X) is ______
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 ______
A card is chosen from a well-shuffled pack of cards. The probability of getting an ace of spade or a jack of diamond 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 ______.
For the following distribution function F(x) of a rv.x.
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| F(x) | 0.2 | 0.37 | 0.48 | 0.62 | 0.85 | 1 |
P(3 < x < 5) =
Find the probability of getting the sum as a perfect square number when two dice are thrown together.
