# Question: For determining the half lives of radioactive isotopes it is important

For determining the half-lives of radioactive isotopes, it is important to know what the background radiation is for a given detector over a certain period. A γ-ray detection experiment over 300 one-second intervals yielded the following data:

Do these look like observations of a Poisson random variable with mean λ = 3? To answer this question, do the following:

- Find the frequencies of 0, 1, 2, . . . , 8.

- Calculate the sample mean and sample variance. Are they approximately equal to each other?

- Construct a probability histogram with λ = 3 and a relative frequency histogram on the same graph.

- Use α = 0.05 and a chi-square goodness-of-fit test to answer this question.

Do these look like observations of a Poisson random variable with mean λ = 3? To answer this question, do the following:

- Find the frequencies of 0, 1, 2, . . . , 8.

- Calculate the sample mean and sample variance. Are they approximately equal to each other?

- Construct a probability histogram with λ = 3 and a relative frequency histogram on the same graph.

- Use α = 0.05 and a chi-square goodness-of-fit test to answer this question.

## Answer to relevant Questions

Prove Theorem 1.1-6. Theorem 1.1-6 If A, B, and C are any three events, then P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) −P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C). Write A ∪ B ∪ C = A ∪ (B ∪ C) A random sample of 50 women who were tested for cholesterol was classified according to age and cholesterol level and grouped into the following contingency table. A student who uses a certain college’s recreational facilities was interested in whether there is a difference between the facilities used by men and those used by women. Use α = 0.05 and the following data to test the ...Different sizes of nails are packaged in “1-pound” boxes. Let Xi equal the weight of a box with nail size C, i = 1, 2, 3, 4, 5, where 4C, 8C, 12C, 16C, and 20C are the sizes of the sinkers from smallest to largest. ...For the data given in Exercise 6.5-4, use a t test to test H0: β = 0 against H1: β > 0 at the α = 0.025 significance level. In Exercise 6.5-4 Ledolter and Hogg (see References) note that percent yields from a certain ...Post your question