5 Written Questions

1. e^(-lamn*x)
2. irrelevant: {a,b} = {b,a}
3. fx(x) * fy(y)
4. Outcomes that cannot occur simultaneously. (disjoint)
5. mean: 0 and Variance: 1

5 Matching Questions

1. Choosing ordered subset of size k withouth replacement from n objets:
2. Continuous Uniform Distribution: F(x) =
3. Discrete Distribution:
4. When considering permutations, the order is:
5. P[A or B or C] =

1. a P[A] + P[B] + P[C] - P[A & B] - P[A & C] - P[B & C] + P[A & B & C]
2. b n! / (n-k)! P(n,k)
3. c integral (a to x) f(x) dx = (x-a) / (b - a)
4. d Can only take on values from a finite infinite sequence.
5. e important: {a,b} does not equal {b,a}

5 Multiple Choice Questions

1. the probability or density function is maximized.
   1. Cumulative Distribution Function:
   2. The Mode of the Distribution is the point where:
   3. Symmetric about the point c if:
   4. For Discrete Uniform Distribution of N points: E[X] =
2. a^2Var[X]
   1. VAR[X+Y] =
   2. P[A or B] =
   3. M'x(0) =
   4. Var[aX + b] =
3. lamn / (lamn - t) t<lamn
   1. Exponential Distribution S(x) =
   2. Exponential Distribution: Mx(t) =
   3. Exponential Distribution F(x) =
   4. Geometric Distribution: Mx(t) =
4. VAR[X] + VAR[Y] + 2*COV[X,Y]
   1. VAR[X+Y] =
   2. P[A or B or C] =
   3. COV[X,X] =
   4. M'x(0) =
5. (1-p) / p
   1. Geometric Distribution: VAR[X] =
   2. Geometric Distribution: E[X] =
   3. Geometric Distribution: Mx(t) =
   4. Binomial Distribution: E[X] =

5 True/False Questions

1. Conditional Probability: P[B] = → P[B(giv)A] P[A] + P[B(giv)A'] P[A']

   True        False

2. told: exponential distribution with mean of 3 (lamna =) → lamn(e^(-lamn*x))

   True        False

3. Exponential Distribution: E[X] & VAR[X] = → 1/lamn & 1/(lamn^2)

   True        False

4. For Discrete Random Variable E[X] = → x1p(x1) + x2p(x2) + .......

   True        False

5. Mx(t) = → E[e^(tx)]

   True        False