Question

. Discrete Distributions. Suppose I flip a coin 40 times. The flips are independent. The probability the coin will come up heads is 40% at each flip. Let X be the number of heads observed in the 40 flips. 26. What is the expected value of X? 27. What is the variance of X? 28. What is P(X 18)? 29. What is P(X 2 18) 30. Using the normal approximation to the binomial with the conti 31. Is the normal approximation appropriate in this case? Why of 32. Using the Poisson approximation to the binomial, what is P(X2 33. Is the Poisson approximation appropriate in this case? Why or nuity correction, what is P(X 2 18)? why not? 18)? why not?

Answer 1

Now a coin is δ1ipped 4° timeo and Hedlips are. Independent. The Pnbe、bihly that the Coin citt Core ap h is 4oo at each dip ouw Co coir coil cane up heads e tina a he loo X- Numben_-6 heads observed in the 49(IPS Nou, vod ia the Nlow eahst is Biml Distibuahion A d's Randun Vantiable X is said to hae a 25 Expedred value ot- X autanc o

2 PCX-19) 40-1 2 1g 10 25 PEX-i] 1.336 x 1o 3.56 46 Xlo3 4.6340 X10구 3. 132 X1o-6 1.1583 X 10-4 4 . S045 x 10-4 4. ol xlo3 a. 507-9 x 10"3 o. O19 6 o o 315 o. O926 O. I 062 0 122 7 o 127 o 1203 -才子6594333 し0123456干8q0i 23456千

う P[X218] = 1-0.6880 О. 312 3 Norma ApproXi hin to Binal O, l We une is appoxion tio to cal aulele P(13) 9-S 。?(270.645) 亞( 2 ( ) o 64 5 0.2579 几 2- 几

2 nni, (l-a)", de-A , l-식→1.ao, n74 几 out np maion 's so几 1-0,659 =0.340 As in the n Cane nomel approximhio we can cleant cohere ao actual PCx>/3)= 0.312 Now the volum hao a-bita&dij.nen ce 2 Noral appaxima hon is not appopriate in this To the Poisii appoximation core ue 2ua cane the main nea son bein p264 is omal