Estimate the PDF of X= U₁U₂ where U, and U₂ are uniform random variables. (Assume U, and U₂ are uniform random variables on the interval [0,1].) Refer to Example 2.1 and the code in Figure 2.7. • Use rng(e) at the start of the script to ensure the same random numbers are generated each time. (Not rand('state',0) as described in the textbook, which is from a previous version of MATLAB.) • Use 1000 realizations. • Use bins centered at 0, 0.1, 0.2..... 1. • Save the random variable X in the variable named x (lowercase). • Save the histogram in the variable named h. • Save the PDF in the variable named pxest. Recall that the PDF is the histogram values divided by the total number of realizations, then divided by the bin width.

Write a function in Python to perform a two sample t-test. The t-test should be unpaired and you may assume that the samples have equal variance. The function should have: specify a choice of alternative hypotheses by giving arguments “two-sided”, “less”, or “greater”. If no such alternative is given, then the default should be “two-sided” specify a parameter mu indicating the true difference in means under the null hypothesis. If unspecified, the default should be mu=0. result should be a dict with the labeled values of the t-statistic and the p-value function should be my_ttest(x,y,mu,alternative), where x and y are the two samples being compared. use the function scipy.stats.t.cdf to calculate p-values generate random samples for testing using npr.normal

) The probability of event A occurring is 5/10. The probability of event B occurring is 5/10. What is the Entropy of this system?

please show the work how you fill the table using the above given. thanks

Please provide workable code in python and show the output

Suppose X|Y=1 is a Uniform(0,4) density, X|Y=0 is a Uniform(2,6) density, and P(Y=1) = 2/3. Calculate the Bayes error, i.e., the error rate of the Bayes classifier (you may leave your answer as a fraction).

Can I get help with doing problem A and C in the image. With details on how to do it. Thank you.

Using the MATLAB editor, make a script m-file for the following: The distance an object with constant acceleration has traveled is given by: d = x0 + vt + 0.5at2 And that x0 = 2.25 meters, v = -0.37 meters/sec and a = 0.32 meters/sec2 For values of t from 0 to 45 sec in increments of 3 secMake variables for x0, v and a, and assign valuesFind the values of d in metersDisplay the results on a x-y scatter plot With t the independent variable plotted on the x axisAnd d the dependent variable plotted on the y axisInclude units within the labels

please please help

Below is the questions