Advertisements
Advertisements
Question
Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its inverse images
Solution
Let X is the random variable that denotes the number of tails when three coins are tossed simultaneously.
Sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
∴ ‘X’ takes the values 0, 1, 2, 3
i.e., (HHH) = 0
X(HHT, HTH, THH) = 1
X(HTT, THT, TTH) = 2
X(TTT) = 3
| Values of the random variable | 0 | 1 | 2 | 3 | Total |
| Number of elements in inverse image | 1 | 3 | 3 | 1 | 8 |
APPEARS IN
RELATED QUESTIONS
An urn contains 5 mangoes and 4 apples. Three fruits are taken at random. If the number of apples taken is a random variable, then find the values of the random variable and number of points in its inverse images
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
Construct cumulative distribution function for the given probability distribution.
| X | 0 | 1 | 2 | 3 |
| P(X = x) | 0.3 | 0. | 0.4 | 0.1 |
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 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 |
Evaluate p(x < 6), p(x ≥ 6) and p(0 < x < 5)
Explain the distribution function of a random variable
Explain the terms probability density function
State the properties of 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:
If the random variable takes negative values, then the negative values will have
Choose the correct alternative:
A set of numerical values assigned to a sample space is called
Choose the correct alternative:
A variable which can assume finite or countably infinite number of values is known as
Choose the correct alternative:
The height of persons in a country is a random variable of the type
Let X be a random variable with a cumulative distribution function.
F(x) = `{{:(0",", "if" x < 0),(x/8",", "if" 0 ≤ x ≤ 1),(1/4 + x/8",", "if" 1 ≤ x ≤ 2),(3/4 + x/12",", "if" 2 ≤ x < 3),(1",", "for" 3 ≤ x):}`
Is X a discrete random variable? Justify your answer
The p.d.f. of X is defined as
f(x) = `{{:("k"",", "for" 0 < x ≤ 4),(0",", "otherwise"):}`
Find the value of k and also find P(2 ≤ X ≤ 4)
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)
