This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
❌ Incorrect. Your calculation P(x=0)=(2)^0 · (2.718)^2 is incorrect. For a Poisson distribution, the probability mass function for P(X=k) is given by: P(X=k) = e^- ^kk! In the previous problem (4c), we found = 2. To find P(X=0), we substitute k=0 and =2 into the formula: P(X=0) = e^-2 (2)^00! Since (2)^0 = 1 and 0! = 1: P(X=0) = e^-2 Using e ≈ 2.718: P(X=0) ≈ (2.718)^-2 P(X=0) ≈ (1)/((2.718)^2) P(X=0) ≈ (1)/(7.387524) P(X=0) ≈ 0.135335 Your calculation used (2.718)^2 instead of (2.718)^-2, which resulted in a value greater than 1, which cannot be a probability. Last free one today — make it count tomorrow, or type /upgrade for unlimited.