Q1:Show that: If X1, X2, ,X, are independent random variables and X = X1 + X +...+ X, , then 02: What is the expectation and the variance of RV X, where X represents the out come throwing a die? 03: Find the expectation and the variance of X, where X is binomial random variable X - Binomial(n, p), Var(X)?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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HW3.pptx >
Q1:Show that: If X1, X2, ,X, are independent random variables and
X = X1 + X2 + + X, , then
Q2: What is the expectation and the veriance of RV X, where X represents the out come throwing a die?
03: Find the expectation and the variance of X, where X is binomial random variable
X - Binomial(n, p), Var(X)?
1.
Chapnera
Q4:
Let X be a discrete random variable with range Rx = {1, 2, 3, ...}.
Suppose the PMF of X is given by
Px (k) =
1
for k = 1, 2, 3, ...
a) Find and plot the CDF of X, Fx(x).
b) Find P(1 <X < 3).
Chapner3
Functions of Random Variables
Q5: Example. Let Rx = {0,
T T 37
, such that
4 2
4
Find Elsin(X)-
Q6: A machine produces a defected items with a probability of 0.1. What is the probability that in a sample of three
item will have at most one item defected?
Q7: For any independent X, and Y random variables, E[XY]=E[XJE[Y). Show that?
QB: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E(X), E[X^2), E[X]^2.
3
II](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2652f62f-82f4-4a11-92f4-f5fcd8d44450%2Ff6b19b5e-4e14-4c73-be9d-c32ecf337f4e%2Fzesiwzb_processed.jpeg&w=3840&q=75)
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