Advertisements
Advertisements
प्रश्न
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:(1/10, x = 2"," 5),(1/5, x = 0"," 1"," 3"," 4):}`
उत्तर
Probability mass function
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| F(x) | `1/5` | `1/5` | `1/10` | `1/5` | `1/5` | `1/10 |
Mean: `mu = "E"("X")`
= `sum x f(x)`
= `0 xx 1/5 + 1 xx 1/5 + 2 xx 1/10 + 3 xx 1/5 + 4 xx 1/5 + 5 xx 1/10`
= `0 + 1/5 + 2/10 + 3/5 + 4/5 + 5/10`
= `23/10`
= 2.3
Variance: `"E"("X"^2)`
= `sum x^2 f(x)`
= `0^2 xx 1/5 + 1^2 xx 1/5 + 2^2 xx 1/10 + 3^2 xx 1/5 + 4^2 xx 1/5 + 5^2 xx 1/10`
= `0 + 1/5 + 4/10 + 9/5 + 16/5 + 25/10`
= `81/10`
= 8.1
Var(X)= E(X2) – [E(X)]2
= 8.1 – (2.3)2
= 8.1 – 5.29
= 2.81
APPEARS IN
संबंधित प्रश्न
For the random variable X with the given probability mass function as below, find the mean and variance.
`f(x) = {{:((4 - x)/6, x = 1"," 2"," 3),(0, "otherwise"):}`
Four fair coins are tossed once. Find the probability mass function, mean and variance for a number of heads that occurred
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
The probability density function of the random variable X is given by
`f(x) = {{:(16x"e"^(-4x), x > 0),(0, x ≤ 0):}`
find the mean and variance of X
Choose the correct alternative:
Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins ₹ 36, otherwise he loses ₹ k2, where k is the face that comes up k = {1, 2, 3, 4, 5}. The expected amount to win at this game in ₹ is
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 X is a binomial random variable with I expected value 6 and variance 2.4, Then P(X = 5) is
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
State the definition of Mathematical expectation using continuous random variable
In a business venture a man can make a profit of ₹ 2,000 with a probability of 0.4 or have a loss of ₹ 1,000 with a probability of 0.6. What is his expected, variance and standard deviation of profit?
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:
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are
Choose the correct alternative:
Probability which explains x is equal to or less than a particular value is classified as
Choose the correct alternative:
A discrete probability distribution may be represented by
Choose the correct alternative:
E[X – E(X)]2 is
Prove that if E(X) = 0, then V(X) = E(X2)
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
Prove that V(aX) = a2V(X)
