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1. Let U and X be random variables, where U is Uniformly distributed (0,1). Given U=u, X has an exponential distribution with parameter =1/u.
(a) Find the joint density of U and X.
(b) Find E[UX]
2. Let (Xn) be a sequence of random variables. Suppose that for every ab i.o.} = 0. Show that lim_n->infinity{Xn} exists a.e., but may be infinite.
[Hint: Consider rational a and b first.]
Is the dependent variable discrete or continuous? interval, or ratio) is used to measure the dependent variable?
A and B are two intersecting sets, and a, b, ab, and x represent the usual symbols for the number of elements contained in the four defined areas of the associated Venn Diagram. Find the values of ab and a if:
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A particle is in the ground state of a box with sides x = +/- a. Very suddenly the sides of the box are moved to x = +/- b(b >a). What is the probability that the particle will be found in the ground state for the new potential? What is the probab..
Plot the market-share data. (b) Describe the trend (if any) and discuss possible causes. (c) Fit three trends (linear, exponential, quadratic).
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Use methods of undetermined coefficients to find one solution of:
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question 1 draw ogives from the following data and measure the median value. verify it by actual calculation.central
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