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When An Estimate Of P^ Is Known.

How do I calculate the interest rate (R) if I know the EMI, tenure (N), and Principal (P) ?

It’s very simple with the help of excel. Follow this easy 8 step process on excel to calculate the interest rate (Don’t worry it will take less than 180 seconds to complete it!)Let us consider that your Principal(P) is 10 lakhs,Tenure(N) is 240 months andEmi is Rs 14,000Step 1: Go to excel,Step 2: Enter the actual Principal (P)Step 3: Enter any random number for interest rate (R). (preferably between 6–20)Step 4: Enter tenure (N) (in months)Step 5: Copy the following formula for EMI. (you just need to edit the cell number and paste the formula)=(A2*(B2/1200)*(1+(B2/1200))^C2)/(((1+(B2/1200))^C2)-1)What’s next???? It’s time to use GoalSeek tool :) :)Excel has given us a very powerful and user-friendly function known as the GoalSeek function.Step 6: Go to Data menu in the Menu Bar >> What if Analysis >> GoalseekStep 7: On clicking the GoalSeek option, a small window will pop up.In “Set Cell”- select the cell, containing the EMI value. In my example, it’s cell D4.In “To Value”- enter your actual EMI (the EMI that you already know- In our example- Rs14,000)(so now you have the values you already know i.e. Principal, tenure, and EMI and it’s time to know the interest rate…….)Step 8: In “By Changing Cell”- select the cell containing interest rate value. In my example, it’s cell C4.(Click on “OK” and it’s done… you have your answer)Let me give you a short video for the same :

Why must we use the point estimate pˆ in the calculation of the standard error when producing a confidence?

When population proportion is unknown, p^ is used in the calculation of the SE
When both population proportion (p) and sample proportion (p^) are known p is preferred to p^ in the calculation of SE

How do I compute a maximum likelihood estimate for a beta distribution whose mean is known to be one-half?

Stirling's approximation is only valid asymptotically.  You can use it to  get a starting point for whatever numerical method you'll use to get the actual estimates, but it's not good on its own.

What is the Maximum Likelihood Estimator of p?

MLE is a method in statistics for estimating parameter(s) of a model for a given data. The basic intuition behind the MLE is that estimate which explains the data best, will be the best estimator.The main advantage of MLE is that it has best asymptotic property. It means that when the data increases, the estimate converge faster towards population parameter. We use MLE for many methods in statistics. I have explained the general steps we follow to find an estimate for the parameter.Step 1: Make an assumption about the data generating function.Step 2: Formulate the likelihood function for the data using the data generating function. The likelihood function is nothing but probability of observing this data given the parameters ([math]P (D|\theta)[/math]). The parameters are depends on our assumptions and data generating function.Step 3: Find an estimator for the parameter using optimization technique. Find the estimate which maximize the likelihood function. This is the reason, we name the estimator calculated using MLE is M-estimator.Example 1: We have tossed a coin n times and observed k heads. Here, we consider head is success and tail is failure.Step 1: The assumption is coin follows Bernoulli distribution function.Step 2: The likelihood function is binomial distribution function ([math]P (D|\theta)[/math]) in this case. We need to find out the best estimate for p (Probability of getting head) given that k of n tosses are Heads.Step 3: M- estimator is[math]\hat{P} = \dfrac{k}{n} \tag{1}[/math]

3 Math Questions that I really really need help with Please?

(1) True or False; For the following n=10
Consider a 90% confidence interval for u, assume o is not known. For which sample size n=10 or
n=20, is the confidence interval longer?
True; n=10 would give the longer interval
False; n=10 would not give the longer interval

(2) What percentage of college students are attending a college in the state where they grew up? Let p be the proportion of college students from the same state as that in which the college resides. If no preliminary study is made to estimate p, how large a sample is needed to be 90% sure that the point estimate (p hat) will be within a distance of 0.07 from p?

a; 138
b; 340
c; 139
d; 196


(3) A preliminary study shows that approximately 71% of college students grew up in the same state as that in which they college resides. Answer the previous question using the estimate for p.

a; 114
b; 113
c; 139
d; 280

Under the ideal conditions a certain bacteria population is known to double every 3 hours. Suppose there are initially 1000 bacteria.?

a) what is the size of the population after 9 hours?

b) what is the size of the population after t hours?

c) Estimate the size of the population after 19 hours.

Please help with statistics question?

The random variable in question is the time taken to complete the drill by an individual (randomly selected) player. Assuming this random variable, which I'll denote X, is normally distribute. Let M denote the (unknown) population mean. Let m denote the population mean (for this case, 8).

We construct a new variable,

Z = (M - m) / [3 / sqrt(144)] = = 4 (M - m)

which then obeys the standard normal distribution.

We are looking for a value z such that P(-z < Z < z) = 0.95. To find this value using the table, we first use the symmetry of the standard normal distribution about its (zero) mean to write:

0.95 = P(-z < Z < z) = 2 P(0 < Z < z) = 2 [P(Z < z) - P(Z <= 0)] = 2 [P(Z < z) - 0.5] = 2 P(Z
so P(Z < z) = 1.95 / 2 = 0.9750, which gives us the estimate z = 1.96.

Therefore, the confidence interval for M is [m - z/4, m + z/4] = [7.51, 8.49].

B. Not sure how to do the said "estimate." If we take the midpoint of the confidence interval as the estimate, we end up with M = m. A more pessimistic estimate would be closer to 7.51 than to 8.49.

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