49. Sigma notation Evaluate the following expressions. 5 Σ (2p+p²) p=1 g.
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- H0: μ = 100 Ha: μ ≠ 100 Alpha=0.01, sigma=10, n = 100, x_bar=102 Calculate p-value)7 Irue/ False L(t%cos4t) = L(t%2)L(cos4t).Sal knows that parties of people on average spend 75 minutes at their restaurant. They wonder if this average is significantly different on the weekends. They found the average time spent by the 30 parties which dined there this weekend was 82 minutes with a SD of 17 minutes. Assume an alpha of .05. Calculate Cohens d. Calculate r^2.
- 1..Consider that a game involves the spinning of a dial which is not fair. As the dial is not fair, after spinning it is more likely to point in any particular direction than another. Suppose that the movement of a dial, X, can be modelled by the following probabilityfunction f(x) = A sin x; 0 ≤ x ≤ π. (i) Determine the value of A so that f(x) is a pdf (ii) Calculate E(X) and Var(X).3.1 Area under the curve, Part I: Find the probability of each of the following, if Z~N(μ = 0,σ = 1).(please round any numerical answers to 4 decimal places)d) P(| Z | >2) =Give at least one reason why the following statements are incorrect.a) If X ~ Bi(4, p), P(X<=2) = P(X>=2) for any pb) If X ~ Po(5), then P(X > 3) = P(X = 4) + P(X = 5). c) If X is continuous quantitative,then P(X<=1) = P(X = 0) + P(X = 1). d) If 2 X ~ N(population mean , (population standard deviation)^2) and a > 0, then P( a<=X-population standard deviation<=2a) = 2P(Z<=a/population standard deviation) -1.e) chi-squared of (k) is symmetrical with respect to k.
- -What is the probability of obtaining a z value less than 1.3? -What is the probability of obtaining a z value more than 1.75? -What is the probability of obtaining a z value between -2 and -1.35? -Find the value of z such that the area to the left of z is 0.8178. -Find the value of z such that the area to the right of z is 0.0305. -What is the value of z0 if P(z ≤ z0) = 0.1507? -What is the value of z if the area between -z and z is 0.74?Sigma (n=0 to n=100) ((n+4)/2))E(Yn)? Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0 and limnYn =0a.s.