Suppose that X and Y have the joint probability distribution shown to the right.(a) Find the marginal distribution of X.(b) Find the marginal distribution of Y.f(x,y)x240.0270.24330.0450.40550.0280.252

Step 1:To find the marginal distributions from the given joint probability distribution table, we…

Answered: Suppose that X and Y have the joint…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 26E

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Respiratory 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.
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Suppose that X and Y have the joint probability distribution shown to the right. (a) Find the marginal distribution of X. (b) Find the marginal distribution of Y. f(x,y) x 2 4 0.027 0.243 3 0.045 0.405 5 0.028 0.252