F is a random variable with u = 5 and v = 3 degrees of freedom. What is the probability that F is bigger than .1289?
3. If a random variable Y has a Chi-square distribution with 9 degrees of freedom. a) The mean of the distribution is b) The standard deviation of the distribution is c) The probability, p( y = 5) = d) The probability, P(Y>8 ) = e) the probability, p( y < 2) = _
3. What is the probability that a T random vaiable with 8 degrees of freedom is equal to 1.86 A. 0 B. 0.05 C. 0.95 D. 1 E. Answer not here 4. Consider a random number generator that has the continuous unifom pdf f(x) = 1 for 0x 1 Recall that u (a+b)/2 and o2 average of n 36 of these random numbers. According to the Central Limit Theorem, what is P(X< 40)? (b-a)/12 for this pdf where a 0...
Find the probability that a random variable having a t distribution with 16 degrees of freedom is greater than 1.746 and less than 2.120. a. 0.025 b. 0.045 c. 0.05 d. 0.100 e. 0.95
Let ? be Student’s ? distributed random variable with ? > 2 degrees of freedom. Find ?[?^2]
Let t be a t-random variable. P(t>a) 0.025 and 12 degrees of freedom. Find a. P(t < a) 0.05 and 21 degrees of freedom. Find a. P(-a < t<a) = 0.95 and 27 degrees of freedom. Find a. For 15 degrees of freedom, find P(t < 1.753) For 22 degrees of freedom, find P(-2.074 < t < 2.074). Use Excel function =t.dist to find P(t<-2.86) with df 25 Use Excel function =t.dist.rt to find P(t > 1.33) with df 29...
Consider a Chi-square random variable with 15 degrees of freedom and 0.1 level of significance. Which of the following test statistic values will result in rejection of the null hypothesis? (1) 21.1. (2) 18.5. (3) 19.8. (4) 23.5. (5) 2.7.
Show that for p = 1 degrees of freedom a Student-t random variable has the Cauchy distribution.
Let Yn be a chi square random variable with n degrees of freedom, and let Xn = Yn / n2. Find the limiting distribution of Xn.
3. An energy production index (V) is a continuous random variable with pdf. 3v2 f(v) =- for 0 Sv32 Find: a) u b)0% c) Pr(V<1) d) Pr(0.5< V <1.5) e) Pr(V=1.25) 4. Referring to problem 3, a different but related index (W) is related to V by the relationship W-3V +8. Find c. Pr(10< W<20)
Let Y1, Y2,. . , Yn be a random sample from the population with pdf f(u:)elsewhere (a) If WIn Yi, show that W, follows an exponential distribution with mean 1/0. (b) Show that 2θΣηι W, follows a χ2 distribution with 2n degrees of freedom. (c) It turns out that if X2 distribution with v degrees of freedom, then E( Use this to show