5. a).lA pair of dice is rolled until the sum is either 7 or 11 (the probability of rolling 7 or11 is 2/9). Let X be the number of rolls before the final roll.i) Determine the formula for Pr(X = n).ii) Determine the average number of rolls before the final roll.x²-9b) [po A random variable X has the cumulative distribution function F (x) =3 < x < 5.on16i) Find a such that Pr (a < X)ii) Find the probability density function for X.Suppose that the life span of a certain automobile tire is normally distributed, withu = 25, 000 miles and o =2000 miles. Find the probability that a tire will last between 28,000and 30,000 miles.A(-2),A(2)TABLE 1 Areas under the Standard Normal Curve.00.01.02.03.04.05.06.07.08.090.0.0000.0040.0080.0120.0160.0199.0239.0279.0319.03590.1.0398.0438.0478.0517.0557.0596.0636.0675.0714.07540.2.0793.0832.0871.0910.0948.0987.1026.1064.1103.11410.3.1179.1217.1255.1293.1331.1368.1406.1443.1480.15170.4.1554.1591.1628.1664.1700.1736.1772.1808.1844.18790.5.1915.1950.1985.2019.2054.2088.2123.2157.2190.22240.6.2258.2291.2324.2357.2389.2422.2454.2486.2518.2549072704272427612704

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5. a) 11 is 2/9). Let X be the number of rolls before the final roll. lA pair of dice is rolled until the sum is either 7 or 11 (the probability of rolling 7 or i) Determine the formula for Pr(X = n). ii) Determine the average number of rolls before the final roll.

5. a) 11 is 2/9). Let X be the number of rolls before the final roll. lA pair of dice is rolled until the sum is either 7 or 11 (the probability of rolling 7 or i) Determine the formula for Pr(X = n). ii) Determine the average number of rolls before the final roll.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

5. a).
lA pair of dice is rolled until the sum is either 7 or 11 (the probability of rolling 7 or
11 is 2/9). Let X be the number of rolls before the final roll.
i) Determine the formula for Pr(X = n).
ii) Determine the average number of rolls before the final roll.
x²-9
b) [po A random variable X has the cumulative distribution function F (x) =
3 < x < 5.
on
16
i) Find a such that Pr (a < X)
ii) Find the probability density function for X.
Suppose that the life span of a certain automobile tire is normally distributed, with
u = 25, 000 miles and o =
2000 miles. Find the probability that a tire will last between 28,000
and 30,000 miles.
A(-2),
A(2)
TABLE 1 Areas under the Standard Normal Curve
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
0.0
.0000
.0040
.0080
.0120
.0160
.0199
.0239
.0279
.0319
.0359
0.1
.0398
.0438
.0478
.0517
.0557
.0596
.0636
.0675
.0714
.0754
0.2
.0793
.0832
.0871
.0910
.0948
.0987
.1026
.1064
.1103
.1141
0.3
.1179
.1217
.1255
.1293
.1331
.1368
.1406
.1443
.1480
.1517
0.4
.1554
.1591
.1628
.1664
.1700
.1736
.1772
.1808
.1844
.1879
0.5
.1915
.1950
.1985
.2019
.2054
.2088
.2123
.2157
.2190
.2224
0.6
.2258
.2291
.2324
.2357
.2389
.2422
.2454
.2486
.2518
.2549
07
2704
2724
2761
2704

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