六、Suppose X_1, X_2, , X_10 are independent random variables and follow N(0, 1). Let S = X_1+X_2+X_3+X_4+X_5 and W = X_6^2+X_7^2+X_8^2+X_9^2+X_10^2. What is the probability P(S/√W > 4.0324)? (Rounded to third place.) (10%)

八、Bowl B₁ contains 2 white chips, bowl B₂ contains 2 red chips, bowl B₃ contains 2 white and 2 red chips, and bowl B₄ contains 3 white chips and 1 red chip. The probabilities of selecting bowl B₁, B₂, B₃, or B₄ are 1/2, 1/4, 1/8, and 1/8, respectively. A bowl is selected using these probabilities, and a chip is then drawn random. Find (a) \(\mathrm{P}(\mathrm{W})\) , the probability of drawing a white chip. \((10\%)\)

六、Suppose $X_1, X_2, \ldots, X_{10}$ are independent random variables and follow N(0, 1). Let $S = X_1+X_2+X_3+X_4+X_5$ and $W = X_6^2+X_7^2+X_8^2+X_9^2+X_{10}^2$. What is the probability $P(S/\sqrt{W} > 4.0324)$? (Rounded to third place.) (10%)

相關申論題

相關試卷