Advertisements
Advertisements
Question
A lottery with 600 tickets gives one prize of ₹ 200, four prizes of ₹ 100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket
Advertisements
Solution
Given, total number of tickets = 600
Prizes to be given: One prize of Rs. 200
Four prizes of ₹ 100
Six prizes of ₹ 50
Let ‘X’ be the random variable denotes the winning amount and it can take the values 200, 100 and 50.
Probability of winning ₹ 200 = `1/600`
Probability of winning ₹ 100 = `4/600`
Probability of winning ₹ 50 = `6/600`
∴ Probability mass function is
| x | 200 | 100 | 50 |
| F(x) | `1/600` | `4/600` | `6/600` |
∴ E(X) = 200 `sum x f(x)`
= `200/600 + 400/600 + 300/600`
= `900/600`
= 1.5
Expected winning amount = Amount won – Cost of lottery
= 1.50 – 2.00
= – 0.50
i.e., Loss of ₹ 0.50
APPEARS IN
RELATED QUESTIONS
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(1/2 "e"^(x/2), "for" x > 0),(0, "otherwise"):}`
Two balls are drawn in succession without replacement from an urn containing four red balls and three black balls. Let X be the possible outcomes drawing red balls. Find the probability mass function and mean for X
The time to failure in thousands of hours of an electronic equipment used in a manufactured computer has the density function
`f(x) = {{:(3"e"^(-3x), x > 0),(0, "eleswhere"):}`
Find the expected life of this electronic equipment
Choose the correct alternative:
A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is
Choose the correct alternative:
If P(X = 0) = 1 – P(X = 1). If E[X] = 3 Var(X), then P(X = 0) is
Find the expected value for the random variable of an unbiased die
Let X be a random variable defining number of students getting A grade. Find the expected value of X from the given table:
| X = x | 0 | 1 | 2 | 3 |
| P(X = x) | 0.2 | 0.1 | 0.4 | 0.3 |
Let X be a continuous random variable with probability density function
`"f"_x(x) = {{:(2x",", 0 ≤ x ≤ 1),(0",", "otherwise"):}`
Find the expected value of X
In investment, a man can make a profit of ₹ 5,000 with a probability of 0.62 or a loss of ₹ 8,000 with a probability of 0.38. Find the expected gain
What do you understand by Mathematical expectation?
Choose the correct alternative:
Given E(X) = 5 and E(Y) = – 2, then E(X – Y) is
Choose the correct alternative:
A discrete probability distribution may be represented by
Choose the correct alternative:
E[X – E(X)]2 is
Choose the correct alternative:
A listing of all the outcomes of an experiment and the probability associated with each outcome is called
Choose the correct alternative:
A discrete probability function p(x) is always non-negative and always lies between
Choose the correct alternative:
The distribution function F(x) is equal to
Prove that V(aX) = a2V(X)
The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
f(x) = `{{:(2"e"^(-2x)",", x > 0),(0",", "otherwise"):}`
Find the expected life of this piece of equipment
