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
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:
Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E(X) and E(Y) respectively are
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
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
Let X be a continuous random variable with probability density function
f(x) = `{{:(3/x^4",", x ≥ 1),(0",", "otherwise"):}`
Find the mean and variance of X
What are the properties of Mathematical expectation?
How do you defi ne variance in terms of Mathematical expectation?
Define Mathematical expectation in terms of discrete random variable
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?
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:
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:
Given E(X) = 5 and E(Y) = – 2, then E(X – Y) is
Choose the correct alternative:
Which of the following is not possible in probability distribution?
Choose the correct alternative:
A discrete probability distribution may be represented by
Choose the correct alternative:
E[X – E(X)]2 is
Prove that V(aX) = a2V(X)
