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if the randon vouable x is unfurly distributed one Cindy siat) Computer { (xul> 3} and...
3 from the exponential distribu- Let X1,ng and tion with pdf be a randon sample of...
3 from the exponential distribu- Let X1,ng and tion with pdf be a randon sample of size n f(x) -4e-4x, 0 < x < oo. Find a. P(0.2< X1,0.2< X2 < 1.5,0.25< X3< 0.8) b. E[2560X1 (X2-0.25)"(Xy-0.25判·
Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2...
Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2 and E[X] = 2.5.
3. Two fair dice are thrown. Let X be the smaller of the two numbers obtained...
3. Two fair dice are thrown. Let X be the smaller of the two numbers obtained (or the common value if the same number is obtained on botih dice). Find the probability mass function of X. Find P(X>3).
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and...
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
o Additional Problem 3: Suppose both X and Y are independent and distributed according to Geo(0.2)....
o Additional Problem 3: Suppose both X and Y are independent and distributed according to Geo(0.2). Compute P(min (X, Y Hint: If X ~ Geo(p), then FX (k) = 1-(1-pt. < 4).
Let X, Y E [0, 1] be distributed according to the joint distribution Íxy (z, y)...
Let X, Y E [0, 1] be distributed according to the joint distribution Íxy (z, y) 6xy2 . Let -XY-3 . Find P(Z < 1 /2)
Problem 2: Let X be a binomially distributed random variable based on n 10 trials with...
Problem 2: Let X be a binomially distributed random variable based on n 10 trials with success probability p 0.3. a) Compute P(X 3 8), P(x-7 and PX> 6) by hand, showing your work.
Assume X is normally distributed with a mean of 7 and a standard deviation of 2....
Assume X is normally distributed with a mean of 7 and a standard deviation of 2. Determine the value for x that solves each of the following Round the answers to 2 decimal places. a) P(X >x) = 0.5 b) P(X > x) = 0.95
Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).
Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).
Suppose that X is an exponential randon variable with λ- 3 and we know how to...
Suppose that X is an exponential randon variable with λ- 3 and we know how to gen- erate X. Explain how you would generate y whose distribution follows an Erlang(k, λ) where k 5 and 3. (Hint: What is the relationship between Erlang(k, A) and Exp(A)?)
3 from the exponential distribu- Let X1,ng and tion with pdf be a randon sample of size n f(x) -4e-4x, 0 < x < oo. Find a. P(0.2< X1,0.2< X2 < 1.5,0.25< X3< 0.8) b. E[2560X1 (X2-0.25)"(Xy-0.25判·
Modify X and apply Markov's inequality to upper bound P(X > 3) when X > 2 and E[X] = 2.5.
3. Two fair dice are thrown. Let X be the smaller of the two numbers obtained (or the common value if the same number is obtained on botih dice). Find the probability mass function of X. Find P(X>3).
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
o Additional Problem 3: Suppose both X and Y are independent and distributed according to Geo(0.2). Compute P(min (X, Y Hint: If X ~ Geo(p), then FX (k) = 1-(1-pt. < 4).
Let X, Y E [0, 1] be distributed according to the joint distribution Íxy (z, y) 6xy2 . Let -XY-3 . Find P(Z < 1 /2)
Problem 2: Let X be a binomially distributed random variable based on n 10 trials with success probability p 0.3. a) Compute P(X 3 8), P(x-7 and PX> 6) by hand, showing your work.
Assume X is normally distributed with a mean of 7 and a standard deviation of 2. Determine the value for x that solves each of the following Round the answers to 2 decimal places. a) P(X >x) = 0.5 b) P(X > x) = 0.95
Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).
Suppose that X is an exponential randon variable with λ- 3 and we know how to gen- erate X. Explain how you would generate y whose distribution follows an Erlang(k, λ) where k 5 and 3. (Hint: What is the relationship between Erlang(k, A) and Exp(A)?)
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