(a) Show that X² is not an unbiased estimator for the area of the square plot p². [Hint: for any rv Y, E[Y²] = V[Y] + E[Y]². Apply this for Y = X.] (b) For what value of k is the estimator X² – kS² unbiased for µ²?

Find the R.M.S. value of Jlogx over the range x = 1 to x = e.

B- For the following data, find f '(2.55), f '(2.7), and f '(2.65) by using the appropriate formula in below for each one. (15Mark) 37 2 X 2.5 Y 1.58114 2.55 1.59687 2.6 2.65 2.7 2.75 1.61245 1.62788 1.64317 1.65831 f₁ = Ji-1+1+1 2h .fi = -6fi-1+20fi+36fi+1-12fi+2+2fi+3 24h fi = fi-2-8fi-1+8fi+1-fi+2 12h

A college language class was chosen for a learning experiment. Using a list of 50 words, the experiment measured the rate of vocabulary memorization at different times during a continuous 6-hour 15 for 1sts6. Find the area between t study session. The average rate of learning for the entire class was inversely proportional to the time spent studying, and was given approximately by V' (t)- the graph of V' and the t-axis over the interval [2.4), and interpret the results The area between the graph of V" and the t-axis over the interval (2.4] is approximately (Round to the nearest whole number as needed) Interpret the results. Choose the correct answer below. GELE A. The area between the graph of V' and the t-axis over the interval [24] is the average number of words learned from t=2 hr to t=4 hr. OB. The area between the graph of V' and the t-axis over the interval (2.4] is the average difference between the rate of learning at 1-2 hr and the rate of learning at t=4 hr. OC. The area…