Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?
Consider the two statements.
S1 : There exist random variables X and Y such that
(E[X - E(X)) (Y - E(Y))])2 > Var[X] Var[Y]
S2 : For all random variables X and Y,
Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]
Which one of the following choices is correct?
A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).
In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.
If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ______