# Statistics

Order Instructions/Description
I need 4 questions done on a software called Rstudio.
I will upload the instructions in Word.

I need the .r format file for this assignment.
You need to comment with your own words to explain what you are doing. Copy codes will give me 0 point for the assignment.
Due 10-25-2015 11:59PM

#———————————————————————–
#Instructions: for plotting the graphs, please use as much ggplot() as
#you can.
#———————————————————————–
#Question 1. Normal Distribution
#1.1 What is the density of 2, given that it is distributed as normal

# distribution with mean 2 and variance 25?

#1.2 What is the cumulative probability of 2, given that it is distributed

# as normal distribution with mean 2 and variance 25?

#1.3 What is the the probability of 0 <= X <= 3, given that x is normally
#distributed with mean 2 and variance 25
#1.4 Plot the cumulative probability graph of a normal distribution with

# mean 2 and variance 25, and find Q1, Median and Q3 of this distribution.

#[Hint: first generate a numeric vector using
#seq(), and use qnorm to generate the corresponding cumulative probabilities
#of this numeric vector]
#———————————————————————–
#Question 2. Bernoulli Distribution
#2.1 What is the probability of tossing a coin 200 times
#2.2 (plot binomial in ggplot):

# A numeric vector is distribuited as binomial distribution

x <- seq(5,15)
#with n=20, p=0.5
#Show the density of x with the ggplot
#———————————————————————–
#Question 3. Geometric Distribution
#Products produced by a machine has a 1.3% defective rate.
#3.1 What is the probability that the first defective occurs
#in the fifth item inspected?
#3.2 What is the probability that the first defective occurs
#in the first two inspections?
#3.3 Generate 100 random samplings for this distribution,
#Find the smaple mean, variance, and graph the samples into a
#histogram plot.
#———————————————————————–
#Question 4. Exponential Distribution
#Given that rate=0.1
#4.1 Draw a graph to show the cumulative probability of 5.
#4.2 Rondomly draw 50,000 observations from this distribution, and calculate
#the sample mean and variance.