PYQs Based Test - 18 : Poisson, Normal and Binomial Distribution

Consider the following probability mass function (p.m.f.) of a random variable X:

p≤ft( x,q ) = ≤ft\{ {*20c q\\ 1 - q\\ 0 } .*20c if X = 0\\ if X = 1\\ otherwise

If q = 0.4, the variance of X is___________.

The probability of a resistor being defective is 0.02. There are 50 such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is ______________.

Let X₁, X₂be two independent normal random variables with means μ₁ , μ₂ and standard deviations σ₁, σ₂,respectively. Consider Y = X₁ – X₂; μ₁ = μ₂ =1, σ₁ = 1, σ₂ = 2. Then,

Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ___________ .

For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal places) is _____