Advertisements
Advertisements
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"):}`
Advertisements
उत्तर
Probability mass function
| x | 1 | 2 | 3 |
| F(x) | `1/2` | `1/3` | `1/6` |
Mean: `mu = "E"("X")`
= `sum x f(x)`
= `1 xx 1/2 + 2 xx 1/3 + 3 xx 1/6`
= `1/2 + 2/3 + 3/6`
= `10/6`
= 1.67
Variance: `"E"("X"^2)`
= `1^2 xx 1/2 + 2^2 xx 1/3 + 3^2 xx 1/6`
= `1/2 + 4/3 + 9/6`
= `20/6`
= 3.33
Var (X) = E(X2) – [E(X)]2
= 3.33 – (1.67)2
= 3.33 – 2.79
= 0.54
APPEARS IN
संबंधित 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):}`
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"):}`
Choose the correct alternative:
On a multiple-choice exam with 3 possible destructive for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is
Choose the correct alternative:
If P(X = 0) = 1 – P(X = 1). If E[X] = 3 Var(X), then P(X = 0) 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
Find the expected value for the random variable of an unbiased die
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
How do you defi ne variance in terms of Mathematical expectation?
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 probability density function may be represented by
Choose the correct alternative:
`int_(-oo)^oo` f(x) dx is always equal to
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
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(X + b) = V(X)
