Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Number of mangoes = 5
Number of Apples = 4
Total number of fruits = 9
Let ‘X’ be the random variable that denotes the number of apples taken, then it takes the values 0, 1, 2, 3
X(MMM) = 0
X(AMM or MAM or MMA) = 1
X(AAM or AMA or MAA) = 2
X(AAA) = 3
| Value of the random variable | 0 | 1 | 2 | 3 | Total |
| Number of elements in inverse image | 10 | 40 | 30 | 4 | 84 |
APPEARS IN
संबंधित प्रश्न
In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images
Two balls are chosen randomly from an urn containing 6 red and 8 black balls. Suppose that we win ₹ 15 for each red ball selected and we lose ₹ 10 for each black ball selected. X denotes the winning amount, then find the values of X and number of points in its inverse images
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
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 the Probability density function
Suppose that the time in minutes that a person has to wait at a certain station for a train is found to be a random phenomenon with a probability function specified by the distribution function
F(x) = `{{:(0",", "for" x ≤ 0),(x/2",", "for" 0 ≤ x < 1),(1/2",", "for" ≤ x < 2),(x/4",", "for" 2 ≤ x < 4),(1",", "for" x ≥ 4):}`
What is the probability that a person will have to wait (i) more than 3 minutes, (ii) less than 3 minutes and (iii) between 1 and 3 minutes?
Define random variable
Explain what are the types of random variable?
Distinguish between discrete and continuous random variables.
Explain the terms probability distribution function
Choose the correct alternative:
If we have f(x) = 2x, 0 ≤ x ≤ 1, then f(x) is a
Choose the correct alternative:
Which one is not an example of random experiment?
Choose the correct alternative:
A set of numerical values assigned to a sample space is called
Choose the correct alternative:
A discrete probability function p(x) is always
Choose the correct alternative:
The probability density function p(x) cannot exceed
The probability function of a random variable X is given by
p(x) = `{{:(1/4",", "for" x = - 2),(1/4",", "for" x = 0),(1/2",", "for" x = 10),(0",", "elsewhere"):}`
Evaluate the following probabilities
P(|X| ≤ 2)
The probability function of a random variable X is given by
p(x) = `{{:(1/4",", "for" x = - 2),(1/4",", "for" x = 0),(1/2",", "for" x = 10),(0",", "elsewhere"):}`
Evaluate the following probabilities
P(0 ≤ X ≤ 10)
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
