Consider that X and Y are independent continuous valued random variables with uniform PDF given by X ~ U(2, 3) and Y ~ U(1, 4). Then P(Y ≤ X) is equal to __________ (rounded off to two decimal places).
Total area = AB × AP.........(From above fig.)
Total area = 1 × 3 = 3
Favourable Area (Fav) = Area of ABCD (i.e. Trapezium)
Favourable Area (Fav) = \(\frac{1}{2}\)(sum of parallel sides) × (Distance between them)
Favourable Area (Fav) = \(\frac{1}{2}\)× (AD + BC)×(AB)
Favourable Area (Fav) = \(\frac{1}{2}\)×(1 + 2) × 1 = 1.5
So P(y ≤ n) = Favourable Area (Fav) / (Total area)
P(y ≤ n) = 1.5/3 = 0.5
Important Questions from Random Variables Basics
The length of time X, needed by an examinee of competition to complete a 1-hour exam, is a random variable with
PDF \(f(x)=\dfrac{6}{5}(x^2+x);0 \le x \le 1.\) , The value of F(0.5) is:If X follows a binomial distribution with n = 6 and \(p=\dfrac{1}{4}\) then the skewness of X is:
If the customers arrive in a shop in Poisson fashion with parameter λ, the fourth raw moment \(\mu_4^{'}\) for the inter-arrival time is:
A discrete random variable X has the probability functions as:
X
0
1
2
3
4
5
6
7
8
f(x)
K
2k
3k
5k
5k
4k
3k
2k
k
The value of E(X) is:What percentage of scores falls within three standard deviations from the mean for the normal variate?
