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- Let X = number of errors per 500 lines of software code. Suppose it is known that E(X) = 4.11 and E(X²) = 17.63. What is Var(X)? Answer:Suppose the relationship between Y and X is given by: Y = 25 - 3X + error By how much does the expected value of Y change if X decreases by 1 unit?Let 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? Density
- The daily price of orange juice 30-day futures is normally distributed. InMarch through April 2007, the mean was 145.5 cents per pound, and standarddeviation = 25.0 cents per pound.4 Assuming the price is independent from day today, find P (x < 100) on the next day.Write an absolute value function f(t) to describe an individual variance from normal body temperature where t is the individual current temperatureAn individual’s income varies with his or her age. The following table shows the median income I of males of different age groups within the United States for 2012. For each age group, let the class midpoint represent theindependent variable, x. For the class “65 years and older,” we will assume that the class midpoint is 69.5. (a) Use a graphing utility to draw a scatter diagram of thedata. Comment on the type of relation that may existbetween the two variables.(b) Use a graphing utility to find the quadratic function ofbest fit that models the relation between age and medianincome.(c) Use the function found in part (b) to determine the age atwhich an individual can expect to earn the most income.(d) Use the function found in part (b) to predict the peakincome earned.(e) With a graphing utility, graph the quadratic function ofbest fit on the scatter diagram.
- A chi square test tells us: a. Whether two continuous variables are correlated with each other. b. Whether two discrete variables are independent of each other c. The amount of variation in one variable explained by the other d. Which categories of one variable are associated with which categories of the other variable(6) Find the mean , variance, autocorrelation function P for the following models: a. Y= 0.6Y+e,- 0.4e t-1 1 1 b.Y, = 2+e;-¿e,s*7 4Find the mean and standard deviation for each uniform continuous model.(Round "Mean" answers to 1 decimal place and "Standard deviation" answers to 4 decimal places. a. U(3, 13) b. U(90, 190) c. U(3, 99)
- The type of battery in Jim's laptop has a lifetime X (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime Y (in years) which follows an exponential distribution with parameter ) =1/4. Find E(XY 2Y). (Answer as a decimal number, and round to 2 decimal places).Assume x is exponentially distributed with a mean of 4. Find: a.P(X=2) b.P(X<2) c.P(X>=2) d.P(2 < X < 4)Suppose that x has an exponential distribution with θ =1.5. Find P(x > 1
