Kindly solve the question

Example 3 The following table contains an incorrect value of f(x). Locate the error, suggest a possible cause and a suitable correction: 2 3 5 6 7 8 9 10 f(x) 37 74 135 226 353. 531 739 1010 1341 173810. (2) The distance D = D() traveled by an object is given in the table below: 8 9 10 11 12 17.453 21.460 - 25.752 30.301 35/084 (i) Find the velocity v(10) by Stirling's formula. (ii) Compare your answer with D(() = - 70 + 7t+ 70e ## [b) From the table below, calculate f '(0.43. ["(0.4) and ( "(04k 5 0.3 0.17835 104 - 18 1477 255 04 0.19312 359 - 73 1836 232 0.21148 591 -30 Use derivatives based on Stirling's formula.Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function f(x) = [*(3-r'), -15251, elsewhere. (a) Determine * that renders f(x) a valid density function.(b) Find the probability that a random error in measurement is less than 1/2.(c) For this particular measurement, it is undesirable if the magnitude of the error (ie., (x]) exceeds 0.8. What is the probability that this occurs? Five independent coin tosses result in HHHHH. It turns out that if the coin is fair the probability of this outcome is (1/2)5 = 0.03125. Does this produce strong evidence that the coin is not fair? Comment and use the concept of P-value discussed inSection 1.1.Consider the density function SAVE, 02, Y= 1); c) (C) P(X > Y);(d) P(X + Y = 4). A coin is flipped until 3 heads in succession occur. List only those elements of the sample space that require 6 or less tosses. Is this a discrete sample space? Explain.Construct a graph of the cumulative distribution function of Exercise 3. 15. Reference: Exercise 3. 15: Find the cumulative distribution function of the random variable X representing the number of defectives in Exercise 3.11. Then using F(x), find (a) P(X = 1); (b) P(0