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Suppose that a trainee soldier shoots a target in an independent manner. If the probability that the target in hit on any one shot is 0.8, what is the probability that the target would he hit an the sixth attempt in fewer than 5 shots in even number of shots

Suppose that a trainee soldier shoots a target in an independent manner. If the probability that the target in hit on any one shot is 0.8, what is the probability that the target would he hit an the sixth attempt in fewer than 5 shots in even number of shots

A First Course in Probability (10th Edition)
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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2:43 PM | 0.5KB/s 4G+ LTE 71 null.pdf 2. 1. atmost one flaw (Assume that number of flaws per unit urea is Poison distributed.) Suppose that a trainee soldier shoots a target in an independent manner. If the probability that the turget is hit on any one shot is 0.8, what is the probability that the target would be hit an the sixth attempt i. ii. in fewer than 5 shots ii. in even numher of shats 4. Consider a sample of size 2 drawn without replacement from an um containing three balls numbered 1, 2 and 3. let X be the number on the fint ball drawn and Y the larger of the two numbers drawn. Find the joint discrete density function of X and Y ii P(X = 1/Y = 3) ii. Find the correlation coefficient of X and Y The joint probability density function of X and Y is given by (+9 OSIS1,0sys2 f(x, y) =3 OSKS1,0 sys2 elsewhere Find the two lines of regression. 5. Let (X), k =1,2, be a sequence of independent random variables defined as P (X = ) = and P(* =-)=;. %3! Examine if the Weak Law of Large Numbers holds for this sequence Two independent samples of 8 and 7 items respectively have the following values of the variables: Sample I: 9 11 13 11 15 9 12 14 Sample 2: 10 12 10 14 9 8 10 Do the two estimates of population variance differ significantly? Given that for (7,6) degrees of freedom the value of F at 5% level of significance is 4.21 6. In a random sample of 500 men from a particular district of UP, 300 are found to he smokers. In ane of 1000 men from another district, 550 are smokers. Do the data indicate that the two districts are significantly different with respect to the prevalence of smoking amang the men. 3. In experiments on pea-breeding, Mendel got the following frequencies of secds: 315 round and yellow, 101 wrinkled and yellow, 108 round and green, 32 wrinkled and green: total 556. Theory predicts that the frequencies should be in the proportion 9:3:3:1. Examine the correspondence hetween theory and experiment. (chi-square at 3 degrees of freedom at 5% level of significance is 7.815)
Transcribed Image Text:2:43 PM | 0.5KB/s 4G+ LTE 71 null.pdf 2. 1. atmost one flaw (Assume that number of flaws per unit urea is Poison distributed.) Suppose that a trainee soldier shoots a target in an independent manner. If the probability that the turget is hit on any one shot is 0.8, what is the probability that the target would be hit an the sixth attempt i. ii. in fewer than 5 shots ii. in even numher of shats 4. Consider a sample of size 2 drawn without replacement from an um containing three balls numbered 1, 2 and 3. let X be the number on the fint ball drawn and Y the larger of the two numbers drawn. Find the joint discrete density function of X and Y ii P(X = 1/Y = 3) ii. Find the correlation coefficient of X and Y The joint probability density function of X and Y is given by (+9 OSIS1,0sys2 f(x, y) =3 OSKS1,0 sys2 elsewhere Find the two lines of regression. 5. Let (X), k =1,2, be a sequence of independent random variables defined as P (X = ) = and P(* =-)=;. %3! Examine if the Weak Law of Large Numbers holds for this sequence Two independent samples of 8 and 7 items respectively have the following values of the variables: Sample I: 9 11 13 11 15 9 12 14 Sample 2: 10 12 10 14 9 8 10 Do the two estimates of population variance differ significantly? Given that for (7,6) degrees of freedom the value of F at 5% level of significance is 4.21 6. In a random sample of 500 men from a particular district of UP, 300 are found to he smokers. In ane of 1000 men from another district, 550 are smokers. Do the data indicate that the two districts are significantly different with respect to the prevalence of smoking amang the men. 3. In experiments on pea-breeding, Mendel got the following frequencies of secds: 315 round and yellow, 101 wrinkled and yellow, 108 round and green, 32 wrinkled and green: total 556. Theory predicts that the frequencies should be in the proportion 9:3:3:1. Examine the correspondence hetween theory and experiment. (chi-square at 3 degrees of freedom at 5% level of significance is 7.815)
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