Let x1,x2,...x n be an iid sample with pdf f(x|0)=0X (® -1) Osxs1,0>0 Find the MLE of 0.
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- Assume a normally distributed population with a mean = 90 and standarddeviation = 12. Be sure to sketch the curves, include formulas & round appropriately. If you select one person at random from this population (M = 90, SD = 12)and find his/her score on this variable to be 68 would you be surprised/consider this score extreme (yes/no)? Why/why not? Be sure to show your work when justifying the answer.24. We have the R output of a one-way ANOVA examining the weight of chicks as a function of their diet. Df Sum Sq Mean Sq F value Pr(>F) 10.81 6.43e-07 *** Diet 3 155863 51954 Residuals 574 2758693 4806 --- Signif. codes: 0.05 '.' 0.1 ' ' 1 0 *** > 0.001 6** > 0.01 *> a. Is the ANOVA significant? Explain. b. Are post hocs necessary? Explain. c. Write the ANOVA summary statement for this output.A model for normal human body temperature, X, when measured orally in °F, is that it is normally distributed, X ~ N (98.2,0.5184). (i) According to the model, what proportion of people have a normal body temperature of 99 °F or more? (ii) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (iii) Let W denote normal human body temperature, when measured orally in °C. Given that W = (X - 32) and X ~ N(98.2,0.5184), what is the distribution of W? (iv) According to the model that you just derived for W, what proportion of people have a normal body temperature of between 36 °C and 36.8 °C?
- A survey on lamb farms was conducted and data were collected on the followingvariables from a random sample of 30 farmers. Y = average live weight of ewes (kg)X1 = area of grazing land (m2) X2 = proportion of farm area that cannot be cultivatedX3 = proportion of area closed for lambs before weaningThe Table below shows the average score of the150 students sampled from the University of the East Europe in the academic year 2020/2021. Score (out of 100) Number of students 40-49 19 50-59 32 60-69 49 70-79 29 80-89 21 Given that Class Frequency 40 - 49 19 50 - 59 32 60 - 69 49 70 - 79 29 80 - 89 21 Class(1) Frequency (f)(2) Mid value (x)(3) f⋅x(4)=(2)×(3) cf(6) 40-49 19 44.5 845.5 19 50-59 32 54.5 1744 51 60-69 49 64.5 3160.5 100 70-79 29 74.5 2160.5 129 80-89 21 84.5 1774.5 150 n=150 ∑f⋅x=9685 Use your results above to comment on the shape of the distribution. Give a reason for you answer.Type II error occurs when an individual fails to reject H0 when H0is false. True or False?
- Obtain 100 (1 x)% confidence limits (for large samples) for the parameter 2 of the f(x, 2) = e-^.^* ; x ; x = 0, 1, 2,... x! Poisson distribution:Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)Plot the gamma distribution by fixing the shape parameter *k* = 3 and setting the scale parameter = 0.5, 1, 2, 3, 4, 5. What is the effect of increasing the scale parameter?