random variable T has a t-distribution with 7 degree of freedom.
Find P(-1<= T<=1).
Suppose P(T<=C=0.9, what is the value of C?
random variable T has a t-distribution with 7 degree of freedom. Find P(-1<= T<=1). Suppose P(T<=C=0.9,...
Assume W is a random variable with a Student t-distribution. Find the following probabilities a.) P[0 ≤ W ≤ 4.303] when W has 2 degrees of freedom b.) P[-2.447 ≤ W ≤ 3.143] when W has 6 degree of freedom c.) P[-1.310 ≤ W ≤ 1.310] when W has 30 degrees of freedom d.) P[-1.96 ≤ W ≤ 1.96] when W has ∞ degrees of freedom Make sure you show your work.
Show that for p = 1 degrees of freedom a Student-t random variable has the Cauchy distribution.
7. Suppose the random variable U has uniform distribution on [0, 1]. Then a second random variable T is chosen to have uniform distribution on [0, U]. Calculate P(T> 1/2)
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...
7. Suppose the random variable U has uniform distribution on [0,1]. Then a second random variable T is chosen to have uniform distribution on [O, U] Calculate P(T > 1/2)
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
5. Suppose X is a discrete random variable that has a geometric distribution with p= 1. a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X> 6). [5] c. Use Chebyshev's Inequality to estimate P(X>6). [5] t> 0 6. Let be the probability density function of the continuous 0 t< 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that...
Consider a t distribution with 7 degrees of freedom. Compute P( t > 1.00). Round your answer to at least three decimal places. Consider a t distribution with 33 degrees of freedom. Find the value of C such that P( -C<t<C)= 0.99. Round your answer to at least three decimal places. P( t > 1.00)= C=
10. Suppose that a random variable X has the uniform distribution on the interval [-2,8). Find the pdf of X and the value of P(O<X<7).
Question 3 Suppose that the random variable X has the Poisson distribution, with P (X0) 0.4. (a) Calculate the probability P (X <3) (b) Calculate the probability P (X-0| X <3) (c) Prove that Y X+1 does not have the Polsson distribution, by calculating P (Y0) Question 4 The random variable X is uniformly distributed on the interval (0, 2) and Y is exponentially distrib- uted with parameter λ (expected value 1 /2). Find the value of λ such that...