Advertisements
Advertisements
प्रश्न
A six sided die is marked ‘2’ on one face, ‘3’ on two of its faces, and ‘4’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images
Advertisements
उत्तर
Six sided die marked ‘2’ on one face, ‘3’ on two faces and ‘4’ on three faces.
When it is thrown twice, we get 36 sample points.
‘X’ denotes sum of the face numbers and the possible values of ‘X’ are 4, 5, 6, 7 and 8
For X = 4, the sample point is (2, 2)
For X = 5, the sample points are (2, 3), (3, 2)
For X = 6, the sample points are (3, 3), (2, 4), (4, 2)
For X = 7, the sample points are (3, 4), (4, 3)
For X = 8, the sample point is (4, 4)
| Value of X | 4 | 5 | 6 | 7 | 8 | Total |
| Number of points in inverse images | 1 | 2 | 3 | 2 | 1 | 9 |
APPEARS IN
संबंधित प्रश्न
The discrete random variable X has the probability function
| X | 1 | 2 | 3 | 4 |
| P(X = x) | k | 2k | 3k | 4k |
Show that k = 0 1
The discrete random variable X has the following probability function.
P(X = x) = `{{:("k"x, x = 2"," 4"," 6),("k"(x - 2), x = 8),(0, "otherwise"):}`
where k is a constant. Show that k = `1/18`
The discrete random variable X has the probability function.
| Value of X = x |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P(x) | 0 | k | 2k | 2k | 3k | k2 | 2k2 | 7k2 + k |
Find k
The distribution of a continuous random variable X in range (– 3, 3) is given by p.d.f.
f(x) = `{{:(1/16(3 + x)^2",", - 3 ≤ x ≤ - 1),(1/16(6 - 2x^2)",", - 1 ≤ x ≤ 1),(1/16(3 - x)^2",", 1 ≤ x ≤ 3):}`
Verify that the area under the curve is unity.
A continuous random variable X has the following distribution function
F(x) = `{{:(0",", "if" x ≤ 1),("k"(x - 1)^4",", "if" 1 < x ≤ 3),(1",", "if" x > 3):}`
Find k
The length of time (in minutes) that a certain person speaks on the telephone is found to be random phenomenon, with a probability function specified by the probability density function f(x) as
f(x) = `{{:("Ae"^((-x)/5)",", "for" x ≥ 0),(0",", "otherwise"):}`
Find the value of A that makes f(x) a p.d.f.
Define random variable
Define dicrete random Variable
Explain the terms probability distribution function
Choose the correct alternative:
A variable that can assume any possible value between two points is called
Choose the correct alternative:
If c is a constant in a continuous probability distribution, then p(x = c) is always equal to
Choose the correct alternative:
Which one is not an example of random experiment?
Choose the correct alternative:
A variable which can assume finite or countably infinite number of values is known as
Choose the correct alternative:
The probability density function p(x) cannot exceed
The probability distribution function of a discrete random variable X is
f(x) = `{{:(2k",", x = 1),(3k",", x = 3),(4k",", x = 5),(0",", "otherwise"):}`
where k is some constant. Find k
The probability distribution function of a discrete random variable X is
f(x) = `{{:(2k",", x = 1),(3k",", x = 3),(4k",", x = 5),(0",", "otherwise"):}`
where k is some constant. Find P(X > 2)
The probability density function of a continuous random variable X is
f(x) = `{{:("a" + "b"x^2",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
where a and b are some constants. Find a and b if E(X) = `3/5`
Consider a random variable X with p.d.f.
f(x) = `{(3x^2",", "if" 0 < x < 1),(0",", "otherwise"):}`
Find E(X) and V(3X – 2)
