Question

distribution. 3. Consider two independent random variables Xį and X2, both following Bernou (a) Find the pmf of W:= X1 + X2 and present it as a table. 15 (b) Now consider a random sample of size 100, X;"9 Bernoulli({). What is the exact distribution of Y := Lizq X;? (Need to specify parameter(s) for full credit.) (c) What is an approximate distribution for Y in part (b) using CLT? (Need to specify param- eter(s) for full credit.) (d) Find a random variable that would (approximate) follow xãf=1 distribution, as a function of Y. (e) Using the distribution found in part (c), find P(54 <Y < 72). Use the standard normal distribution table for full credit. (Continuity correction is not required. Do not round the values you achieved from the table.)

Answer 1

Son Xiaper ( ), xew Ber(3) W Xitxa xu-txa av Bin (2, 3) Malta Mx, tx lit): MACH Mx, 14 .:(}+}et) ( 4şey = (2+ & et) 2 M.Gif represent uniquenen property and * 4 mgf of B12, 2) - W= x,+, W8M12, 3). b) 1.100 , xi wild Ber(?) Troly Exi N Bin (100, ş) 2: Y-ElY), Exi - ElEX). Exi- loox} - Jurns ? TV(EX: Toegex] z - EX-40 WN(O) 2 ekor her NOG 19 c) P (54 <¥¢72) Pile on this) es Scanned with CamScanner Be

1/54 < YC+2). Play ( 2 < ) - ¢(320)-° ( ) = $(6:53) - $(2.85) = 1 - 0.9978 Plsy<Y<72) - 0.00227 Scanned with CamScanner