Probability maximum value of samples from different distributions
Assume you are sampling values at random from two normal distributions, Distribution A and Distribution B. Both distributions have the same standard deviation ? but slightly different means $?_A$ and $?_B$, where $?_A>?_B$. Let $\delta_\mu = ?_A-?_B$.
You?re drawing a total of n samples from these two distribution: q samples from A, and n-q from B. What is the probability that the largest value among the n samples came from Distribution A? Please explain your steps. Assume n is finite and relatively small (<100). Verify your results by calculating the probability that the largest sample comes from A for the following parameters: $n = 6, q = [1,2,3,4,5], ?_A=1001$ and $?_B=1000$, and $?=10$.
Answer
Hi,
Attached is the solutions, with R code in the Appendix. Thanks!
- answered
- 331 views
- $25.00
Related Questions
- Applied Probability
- Probability/statistics
- Spot my mistake and fix it so that it matches with the correct answer. The problem is calculus based.
- Explain how to get the vertical values when $n = 10$, $p = .5$, $\mu = 5$ and $\sigma^2 = 2.5$
- Statisitical Experimental Design Question
- What plots should I use to describe the relationship between these 8 continuous variables?
- Statistical analysis on a 2 dimensional data set
- Please solve the attached problem from my worksheet
