Advertisements
Advertisements
Question
What is the expected value of a game that works as follows: I flip a coin and if tails pay you ₹ 2; if heads pay you ₹ 1. In either case, I also pay you ₹ 0.50
Advertisements
Solution
Let x be the remain variable denoting the amount paying for a game of flip coin then x and takes 2 and 1
P(X = 2) = `1/2` (getting a head)
P(X = 1) = `1/2` (getting a tail)
Hence the probability of X is
| X | 2 | 1 |
| P(X = x) | `1/2` | `1/2` |
Expected value E(X) = `sum_x "P"(x)`
= `(2)(1/2) + 1(1/2)`
= `1 + 1/2`
= `3/2`
Since I pay you ₹ 50 in either case
E(X) = 50 × `3/2` = ₹ 75
APPEARS IN
RELATED QUESTIONS
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
A commuter train arrives punctually at a station every half hour. Each morning, a student leaves his house to the train station. Let X denote the amount of time, in minutes, that the student waits for the train from the time he reaches the train station. It is known that the pdf of X is
`f(x) = {{:(1/30, 0 < x < 30),(0, "elsewhere"):}`
Obtain and interpret the expected value of the random variable X
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
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 |
The following table is describing about the probability mass function of the random variable X
| x | 3 | 4 | 5 |
| P(x) | 0.2 | 0.3 | 0.5 |
Find the standard deviation of x.
State the definition of Mathematical expectation using continuous random variable
A person tosses a coin and is to receive ₹ 4 for a head and is to pay ₹ 2 for a tail. Find the expectation and variance of his gains
Choose the correct alternative:
E[X – E(X)]2 is
Choose the correct alternative:
`int_(-oo)^oo` f(x) dx is always equal to
Choose the correct alternative:
The distribution function F(x) is equal to
