In a binary PAM system for which the two signals occur with unequal probabilities (p and 1p), the optimum detector is specified by Equation (7.5.54). √ebr 2. 1. Determine the average probability of error as a function of (E₁/N) and p. Evaluate the probability of error for p = 0.3 and p = 0.5, with Eb/No = 10. how to find the formule two signals 1-P (7.5.54) occur with unequal probabilities ? step by step explain P AV ~~ In 1 P No P = In

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. Do these data provide convincing statistical evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97? Complete the “State” step for this test. H0: p =  Ha: p   where p = the true proportion of all  that .

Imagine you have two estimators X and Y, for unknown parameter µ. Assume that they are estimated from independent datasets. Let Z = }(X+Y) be the average of these two estimators. To write the symbol µ, you can write mu. For other math notation, you can E[X], Var(X) and (X+Y)/2 or (1/2)(X+Y). Part a - If X and Y are unbiased estimators, E[X] = E[Y] = µ, then is Z unbiased? Explain why or why not. Your explanation should include a short derivation. Part bL Assume Var(X) = Var(Y). Is Z a lower variance or higher variance estimator than X? Explain your answer. Your explanation should include a short derivation.

If P(A) = 0.2, P (B) = 0.4 and P(A|B)) = 0.1 Compute P (AUB) Enter your answer with two decimal places.