Q1) Simulation of Random Variables Distribution a) Generate 30 columns of data (X1, X2, , X30) using excel or any software of your liking, where each column contains 100 random values using U(0,10) (Uniform random variable with a=0 and b=10. ) b) Construct a new random variable Y2= (X1+X2)/2, Y3= (X1+X2+X3)/3, Y10= (X1+X2++X10)/10, Y30=(X1++X30)/30. c) Graph the corresponding histogram of X1, Y1, Y2, Y3, Y4. What do you notice? d) Generate 5 columns of data, where each columns contains 100 points using N(0,1). e) Construct new random variables W1= (X1+X2)/2, W3= (X1+X2+X3)/3, W5=(X1+..+X5)/5. f) Graph the corresponding histograms of the random variables X1, W2, W3, W5. What do you notice. Q2) Confidence Interval Estimation Weight at birth (Kilograms) * Region Weight at birth (Kilograms) Region Mean N Std. Deviation West Bank 3.19383 1661 .550526 Gaza Strip 3.25492 1221 .580198 Total 3.21971 2882 .563997 Legal Age When First Married * Region Crosstabulation Region Total West Bank Gaza Strip Legal Age When First Married Legal Count 3830 2077 5907 % within Region 75.7% 68.3% 72.9% Not legal Count 1232 966 2198 % within Region 24.3% 31.7% 27.1% Total Count 5062 3043 8105 % within Region 100.0% 100.0% 100.0% Refer to the two above tables that were obtained from the recent health survey conducted by PCBS to answer the following questions. a) Construct a 95% confidence interval for the population mean birth weights in Gaza. In your own words define the target population for this parameter of interest. b) Construct a 95% confidence interval or the population mean birth weights in the West Bank. c) Construct a 95% Confidence interval for the difference in the two population means (Population mean of birth weights in Gaza Population mean birth weights for the West Bank). Can you conclude that the population mean of birth weights in Gaza is different than that of the West Bank? Why? d) Construct a 95% Confidence interval for the population percentage of illegal marriages in Gaza. In your own words define the target population for this parameter of interest. e) Construct a 95% confidence interval for the population percentage of illegal marriages in the West Bank. f) Construct a 95% confidence interval for the difference of the population illegal marriages in Gaza and the West Bank. Can you conclude that the difference of the population percentage of illegal marriage in Gaza is higher than that in the West Bank? Why?.