Concept explainers
a.
If
a.
Explanation of Solution
It is given that Y has a beta distribution with parameters
The probability density
The
Therefore, it is proved that
b.
Explain the reason for Part (a), which requires that
b.
Explanation of Solution
The answer in Part (a) has to be satisfied that
c.
Show that, with
c.
Answer to Problem 200SE
It is proved that
Explanation of Solution
The answer in Part (a) is as follows:
Substitute
Therefore, for
d.
Find an expression for
Find the expression that one needs to assume about
d.
Explanation of Solution
The answer in Part (a) is as follows:
Substitute
Therefore, the value of
e.
Use the results in Part (a) to find an expression for
Identify the value of
e.
Explanation of Solution
The result in Part (a) is as follows:
Case1:
Substitute
Thus, in this case one needs to assume that the value of
Case 2:
Substitute
Therefore, the value of
Case3:
Substitute
Thus, value of
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Chapter 4 Solutions
Mathematical Statistics with Applications
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forward3.a. Suppose Var(X1) = 2.25, Var(X2) = 2.56, and Cov(X1, X2) = -0.25. Find the correlation p of X1 and X2. b. Suppose E(Y;) = 1arrow_forward2.11 Let X have the standard normal pdf, fx(x) = (1/√√2π) e¯2²/² (a) Find EX² directly, and then by using the pdf of Y = X2 from Example 2.1.7 and calculating EY. (b) Find the pdf of Y = |X|, and find its mean and variance.arrow_forwardSuppose that a random voltage V supplies a random current I through a constant resistive load. What is the best representation of the correlation between V and I? O a. p(X, Y) = −1 O b. p(X, Y) 0 O d. p(X, Y) = 1arrow_forwardAn M.V.U. is unique in the sense that if T, and T, are 1 M.V.U. estimators for y (0), then T, = T, almost surly. 1arrow_forwardIf Z = ax + by and yis the correlation coefficient between X and Y. Show that (a) o = a°o% +b²o + 2abrox0y (b) y(X, Y) = 20,0yarrow_forward(21) Let X b(12,–) find E(5+6x) and distribution function.arrow_forwardSuppose that X and Y are unknown with E(X) = 20, Var (X) = 4 , E(Y) = 12, and Var (Y) = 16. In addition, suppose that E(XY) = 248. Then what is the correlation of X with Y?arrow_forwardarrow_back_iosarrow_forward_ios
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