Concept explainers
Suppose that Y is a binomial random variable with n > 2 trials and success
Derive
Explanation of Solution
Calculation:
Theorem 3.7:
If Y is a binomial random variable based on n trials and success probability p, then
The random variable Y is binomial random variable having
Consider the term
Add and subtract 3 to the term
Suppose that
It is obvious that,
That is,
The value of
Hence, the expression is
Want to see more full solutions like this?
Chapter 3 Solutions
Mathematical Statistics with Applications
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forwardIf X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2,find P{X1 < X2} and P{X2 < X1}.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning