Question

asked 2021-07-02

An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year’s economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments.

Certificate of deposit

Office complex

Land speculation

Technical school

amp; Strong amp;6,000 amp;15,000 amp;33,000 amp;5,500

amp; Weak amp;6,000 amp;5,000 amp;−17,000 amp;10,000

Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year’s economy has a 40% chance of being strong and a 60% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. b. Determine the expected value of each random variable. c. Which investment has the best expected payoff? the worst? d. Which investment would you select? Explain.

Certificate of deposit

Office complex

Land speculation

Technical school

amp; Strong amp;6,000 amp;15,000 amp;33,000 amp;5,500

amp; Weak amp;6,000 amp;5,000 amp;−17,000 amp;10,000

Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year’s economy has a 40% chance of being strong and a 60% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. b. Determine the expected value of each random variable. c. Which investment has the best expected payoff? the worst? d. Which investment would you select? Explain.

asked 2021-05-14

When σ is unknown and the sample size is \(\displaystyle{n}\geq{30}\), there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When \(\displaystyle{n}\geq{30}\), use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

asked 2021-02-25

We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:

a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.

b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.

c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.

d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.

Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.

a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.

b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.

c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.

d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.

Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.

asked 2021-05-23

Does increasing the sample size make you more confident? You can investigate this question using the Confidence Intervals applet at highschool.bfwpub.com/spa3e. Using a 95% confidence level and sample size n = 20, click "Sample 25" 40 times to select 1000 SRSs and make 1000 confidence intervals. What percent of the intervals captured the true mean μ?μ?