GATE 2023 Engg. Mathematics Quiz 6

Let X ϵ {0, 1} be two independent binary random variables. If P(X = 0) = P and P(Y = 0) = q, then P(X + Y ≥ 1) is equal to

then find the value of at x = 1, y = 2?

f(x) = x, g(x) = ; by using Cauchy mean value theorem mean value for the function in [a,b] will be______.

The value of the integral  is ______.

Find the maximum value of

Parcels from sender S to receiver R pass sequentially through two post –offices. Each post – office has a probability 1/5 of losing an incoming parcel, independently of all other parcel. Given that a parcel is lost, the probability that it was lost by the second post –office is

The equation 5x–2cosx – 1 = 0 is to be solved first by newton Raphson method by taking initial glass x = 0.5 and then bisection method is applied using the initial guess and this new estimate from newton Raphson. The estimated value of the root of equation of the bisection method is _____.