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1. Find the joint p.d.f. of the signal from Exercise 8.5.1 at t1 = 1, t2 = 1.5, and t3 = 2.5. Write the integral formula for P(0 ≤ X(1) ≤ 1, -1 ≤ X(1.5) ≤ 3, 0 ≤ X(2.5) ≤ 2).
Evaluate the above probability numerically.
2. Show that if a 2D Gaussian random vector Y- = (Y1, Y2) has uncorrelated components Y1, Y2, then those components are statistically independent random quantities.
For a standard normal curve, find the z-score that separates the bottom 90% from the top 10%.
Consider the following two columns that describe different types of data: A. Nominal 1. Qualitative B. Discrete 2. Quantitative C. Ordinal D. Continuous. The correctly paired groupings of the two columns is:
the purchasing department of major company has 100 employees 22 of whom have no children 50 of whom have exactly one
Suppose that a car rental agency offers insurance for a week that will cost $10 per day. A minor fender bender will cost $1,200 while a major accident might cost 10,000.
Among a group of 165 students 8 are taking calculus, discrete structures, and computer science; 33 are taking calculus and computer science; 20 are taking calculus and discrete structures; 24 are taking discrete structures and computer science;
What do high and low values of kurtosis imply for the shape of a frequency distribution? Draw a diagram to illustrate your answer.
Population standard deviation is known to be 8 grams. Determine and interpret p-value for testing that mean weight of Take-a-Bite is less than 175 grams.
Test whether there is any change in IQ after the training program. (The absolute value of t for 4 degrees of freedom at 1% level for one-tailed and two tailed tests are 3.747 and 4.604 respectively.
For each player, determine the minimum, the first quartile, the median, the third quartile and the maximum of their home run totals. Use these results to construct comparative box-and-whisker plots.
In the Florida lottery, six numbers from 1 to 53 must be selected. to win the jackpot, the six numbers must match the draw numbers.
a let x and y be independent random variables with moment generating functions ft and gt respectively. let zxy.
Show that if (a_n)[n=1,infinity] and (b_n)[n=1,infinity] are equivalent sequences of rationals, then (a_n)[n=1,infinity] is a Cauchy sequence if and only if (b_n)[n=1,infinity] is a Cauchy sequence.
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