Concept explainers
Let
- a E(Y)
- b V(Y)
- c The distribution of Y
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Chapter 3 Solutions
Mathematical Statistics with Applications
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.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_forwardShow that an equation of the normal line to the graph of a b. b² – a² at the point (a, b) is given by a abarrow_forward
- a. What is the equation of the normal line to the curve 2x3+2y3-9xy=2 at the point (0,1)? b. Graph the function and the normal line.arrow_forwardLet's say p a real function p by: 1 P(x) = 2 x E R a. Calculate the variance of Xarrow_forwardI. The following table gives the distribution of a r.v. X ,where a and B are constants, -2 2 P(X=x) 0.3 0.2 0.1 If E(X)=0, then find E(3x -5)arrow_forward
- Answer c only showing all workings and using the t distribution tablearrow_forwardThe amount of time a service technician needs to change the oil in a car is uniformly distributed between 11 and 21 minutes. Let X = the time needed to change the oil on a car. b. Graph the distribution and find P (x > 19). Round to the nearest tenth.arrow_forwardLet X-T(4) and Y~ x2 (4). The following plot depicts the cumulative distribution functions of X and Y. We don't know which is which. The horizontal lines have values 25% and 75%. We denote by q1 the x-coordinate correponding to the red point and by q2 the x-coordinate corresponding to the blue point. Which of the following statements are true? 1.00 - 0.75 0.50 - 0.25+ 0.00 - The answer is : The cdf of X corresponds to the red curve while the one of Y corresponds to the blue curve. Can you explain why? Densityarrow_forward
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