3. (a) (3 pts.) Determine in how many ways one can place twelve indistinguishable balls in...
3. (a) (3 pts.) Determine in how many ways one can place twelve indistinguishable balls in six boxes in such a way that none of the boxes is empty. (b) (3 pts.) Repeat the exercise from part (a) with r balls and n boxes, where r > n.
Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
O words Question 6 3 pts 6. Magnesuim + Oxygen > Magnesium oxide When 55g of magnesium is oxidized by the presence of oxygen, how many moles of product are produced HTML BIVA..LEE 3.x X, E vo V112pt Paragraph
Part C Figure 1 of 4 > Derive the expression for the periad af ascillatians of the ice cube Express your answer in terms of radius R of the frame, the free-fall acceleration g, and the constant Submit Request Answer Part D Complete previous part(s)
3. Let X be a geometric random variable with parameter p. Prove that P(X >k+r|X > k) = P(X > r). This is called the memoryless property of the geometric random variable.
The probability mass function of a random variable X is given by Px(n)r n- (a) Find c (Hint: use the relationship that Ση_0 n-e) (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3)
Given the product structure diagram below, how many Ws are needed to make each Z? w >ão Ec O 12 Oo o
3. (25 pts) The circuit is at steady state before the switch closes. Determine the capacitor voltage, v(), for t> 0 2 Hin + )20 V 50 2 50 2
Let X, Y be two independent exponential random variables with means 1 and 3, respectively. Find P(X> Y)
3. (10 pts.) X is a Gaussian random variable with E{X} = 2 and Var(X) = 16. Let Y = 3X +1. Determine the probability: Pr(Y > 2)