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
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(2(x - 1), 1 < x ≤ 2),(0, "otherwise"):}`
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"):}`
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.
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
Choose the correct alternative:
Value which is obtained by multiplying possible values of a random variable with a probability of occurrence and is equal to the weighted average is called
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:
An expected value of a random variable is equal to it’s
Choose the correct alternative:
A discrete probability function p(x) is always non-negative and always lies between
Prove that V(aX) = a2V(X)
