PYQs Based Test - 21 : Discrete and Continuous Distribution

The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is _______. [round off to 3 decimal places]

If the probability density function of a random variable x is given by

f(x)=≤ft\{ {*20c {{kx^2}2}& - 1 ≤ x ≤ 1\\ 0&elsewhere, } .

the value of k is ______.

Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is _______

The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is _________

Find the value of λ such that the function f (x) is a valid probability density function. _______

f≤ft( x )*20c = λ ≤ft( x - 1 )≤ft( 2 - x )&for1 ≤ x ≤ 2\\ = 0&otherwise