Probability density function

Testing the Mean for a Sample with Unknown Distribution 2 points possible (graded) Suppose that you observe a sample X1, ..., X, ~ P for some distribution P with continuous cdf. Your goal is to decide between the null and alternative hypotheses Ho : H = 0 HI : H #0. Looking at a histogram, you suspect that X1, ..., X, have a Gaussian distribution. You would like to first test this suspicion. Formally, you would like to decide between the following null and alternative hypotheses: H : P E IN ( 1, 6 ) ) HER, 6 2 20 H : P E IN ( H, o') ) MER, 5 2 20. Which of the following tests should you use to decide between Ho and H;? O Student's T test O Kolmogorov-Smirnov test O Kolmogorov-Lilliefors testIt is 0.831999 Bivariate Fit of Happiness By LifeExpectancy Happiness un 40 45 50 55 60 65 70 80 85 LifeExpectancy Bivariate Normal Ellipse P=0950 Bivariate Normal Ellipse P=0990 Bivariate Normal Ellipse P=0.950 Variable Mean Std Dev Correlation Signit. Prob Number LifeExpectancy 67.83646 11.04193 0.631999 <.0001 happiness bivariate normal ellipse p="0.990" variable mean std dev correlation signit. prob number lifeexpectancy can we conclude that being happier causes people to live longer explain. pts each of the following transition matrices determine whether markov chain with matrix is regular: whose regular or no consider state space and suppose xo="0." find probability x2="2." stationary distribution chain. what proportion time does spend in long run x5="1." expected additional steps until first will return>