A sample of radioactive Thorium emits alpha particles at a rate of 1.5 particles per minute. a) What is the expected average number of alpha particles emitted in 40s? b) What is the probability that 5 particles are emitted in 40s? c) We now divide the interval T=40 in two subintervals. Given ν1 and ν2 the number of particles emitted respectively in the two periods of time T1=30s and T2=10s, what are the following probabilities that νiνi particles are detected in the first and second time intervals? P(ν1=0,ν2=5)= P(ν1=1,ν2=4)= P(ν1=2,ν2=3)= P(ν1=3,ν2=2)= P(ν1=4,ν2=1)= P(ν1=5,ν2=0)=

A sample of radioactive Thorium emits alpha particles at a rate of 1.5 particles per minute. a) What is the expected average number of alpha particles emitted in 40s? b) What is the probability that 5 particles are emitted in 40s? c) We now divide the interval T=40 in two subintervals. Given ν1 and ν2 the number of particles emitted respectively in the two periods of time T1=30s and T2=10s, what are the following probabilities that νiνi particles are detected in the first and second time intervals? P(ν1=0,ν2=5)= P(ν1=1,ν2=4)= P(ν1=2,ν2=3)= P(ν1=3,ν2=2)= P(ν1=4,ν2=1)= P(ν1=5,ν2=0)=

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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Question

A sample of radioactive Thorium emits alpha particles at a rate of 1.5 particles per minute.

a) What is the expected average number of alpha particles emitted in 40s?

b) What is the probability that 5 particles are emitted in 40s?

c) We now divide the interval T=40 in two subintervals. Given ν1 and ν2 the number of particles emitted respectively in the two periods of time T1=30s and T2=10s, what are the following probabilities that νiνi particles are detected in the first and second time intervals?

P(ν1=0,ν2=5)=

P(ν1=1,ν2=4)=

P(ν1=2,ν2=3)=

P(ν1=3,ν2=2)=

P(ν1=4,ν2=1)=

P(ν1=5,ν2=0)=

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