Search & Filtering
Given the normally distributed variable X with mean 18 and standard deviation 2.5, find: (a) P(X < 15); (b) P(17 < X <21); (c) the value of k such that P(X<k) = 0.2578; (d) the value of k such that P (X > k) = 0.1539
the value of k such that P(X<k) = 0.2578
The following data resulted from 5 experimental runa made on four indrpendent variables and a single response y
, we
proved in class that the value of β can be found by minimizing the EPE for the problem, namely E((Y −X^T β)^2), and this minimization gives rise to β = (E(XX^T))^−1E(XY )... (1)
Prove this formula directly from the fact that
E(Y |X) = X^T β... (2)
In particular, (a) multiply both sides of (2) by X (from the left), then (b) take the expectation w.r.t. X on
both sides (i.e. you will get E(XE(Y |X)) = E(XX^T β), and (c) show that this implies formula (1).
normal r.v.s). Define the random vector X = (X1, X2)^T by X1 = G1 and X2 = G1 + G2. Define Y =
X1 + (X2)^2 + Z, where Z is a uniform random variable on [−1, 1] that is independent of both G1 and G2.
Find the best linear model for predicting the output Y from the input X. In other words, find the vector
β = (β1, β2)^T
that minimizes E((Y − hX, βi)^2
). (Note: Thus, we know that the true regression function is
not linear, but we are still attempting to approximate it by a linear function.)
Suppose that discarded cold drink cans are found along a particular road according to a Poisson process, with an average frequency of 3.2 cans every kilometre. What is the probability that a rubbish collector finds at least 2 cold drink cans in a given 200 metre stretch along this road?
the probability that a person has a checking account is 0.74 a saving account is 0.31 and both account is 0.22. Find probability that a randomly selected person has a checking or saving accounts
A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchases right out of the box. In its last model, 85% of customers received fully charged batteries. To simulate arrivals, the company shipped 105 new model laptops to various company sites around the country. Of the 105 laptops shipped, 96 of them arrived reading 100% charged. Do the data provide evidence that this model’s rate is at least as high as the previous model? Test the hypothesis at α = 0.05.
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 39 beats per minute, the mean of the listed pulse rates is x=72.0 beats per minute, and their standard deviation is s=10.7 beats per minute.
a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the females?
b. How many standard deviations is that [the difference found in part (a)]?
c. Convert the pulse rate of 39 beats per minutes to a z score.
d. If we consider pulse rates that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 39 beats per minute significant?
