Probability and complex function: Unit I: Probability and random variables
Exercise 1.10 (Uniform distribution or Rectangular Distribution)
Problems with Answer | Random variables
Probability and complex function: Unit I: Probability and random variables : Exercise 1.10
EXERCISE 1.10
1.
For the rectangular distribution dp = k dx, 1 ≤ x ≤ 2. Show that Arithmetic
mean > Geometric mean > Harmonic mean.
2.
A random variable X is uniformly distributed over (0, 1), find the density of Y
= x2 + 1.
3.
A distribution is given by f (x) = -ɑ ≤ x ≤ ɑ. Find the first four central
moments and obtain β1 and β2.
4.
If X1 and X2 are independent rectangular variates on [0,
1], find the distribution of X1 / X2
5.
If X is a random variable with a continuous distribution function F(x), then
F(x) has a uniform distribution on [0, 1].
6.
If the mgf of a continuous r.v. X is 1/t (e5t - e4t), t ≠
0 what is the distribution of X? What are its mean and variance ?
[Ans.
E[X] = 9/2, Var(X) = 1/12]
7.
If X has uniform distribution in (-ɑ, ɑ), ɑ > 0 find a such that P(| X | <
1) = P(| X | > 1).
[Ans.
ɑ = 2]
8.
If X is uniformly distributed r.v. with mean 1 and variance find P (X < 0).
[Ans. (1/4)]
Probability and complex function: Unit I: Probability and random variables : Tag: : Problems with Answer | Random variables - Exercise 1.10 (Uniform distribution or Rectangular Distribution)
Related Topics
Related Subjects
Probability and complex function
MA3303 3rd Semester EEE Dept | 2021 Regulation | 3rd Semester EEE Dept 2021 Regulation