Understanding Probability & Statistics

[Execute]

Hey everyone!

I had the following problem on mt test & still can't figure out how to do it. Please help me understand it.

Question: A computer has a 32-bit register. The current drawn from the power supply is
i = 0.1 + 0.05k(micro amperes), where k is the number of 1's in the register. Under normal operating conditions, 1's and 0's are equally likely and independent throughout the register. Find the probability that the current falls between 1.2 & 1.4 (micro amperes), inclusive.

Thanks everyone.

 

[quantumdude]

You really are supposed to explain your own thoughts before receiving help here, but I'll start you off by saying that you should use the bounds on the current to find bounds on k.

 

[piercas]

Hello there,

Probability and statistics are essential tools in the field of science and are used to analyze and interpret data. In this case, we can use these tools to solve the problem you have mentioned.

To find the probability that the current falls between 1.2 and 1.4 micro amperes, we need to first understand the distribution of the number of 1's in the register. Since 1's and 0's are equally likely and independent, the distribution will follow a binomial distribution.

Next, we need to calculate the probability of getting a particular number of 1's in the register. This can be done using the binomial probability formula, which is P(k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of bits in the register, k is the number of 1's, and p is the probability of getting a 1.

In this case, n = 32 and p = 0.5. Now, we need to calculate the probability of getting k = 12, 13, or 14 1's in the register. This can be done by plugging in the values in the binomial probability formula and summing them up. The final result will give us the probability of the current falling between 1.2 and 1.4 micro amperes.

I hope this helps you understand the problem better. If you have any further questions, please don't hesitate to ask. Keep practicing and good luck on your test!