L6

Question 1

What type of random variable would the length if a ropes be

Answer 1

A continuous random variable since it is not limited to a set number of alternatives

Question 2

What is the difference between a the probability of a continuous random variable being a value up to including a number and simply up to that number

Answer 2

The difference is infinitely small

Question 3

What is the probability that a continuous random variable has a particular value

Answer 3

As there ate infinite alternatives the probability of a single variable is basically zero

Question 4

What is the probability density function for a continuous variable

Answer 4

PDF is the continuous equivalent of the discrete probability mass function where the integral shows the likelihood of the random variable to appear within an interval

Question 5

What is the area under the entire probability density function

Answer 5

1

Question 6

Describe the continuous uniform distribution

Answer 6

Where the probability is equal for all intervals in a range and zero outside that range

Question 7

How do you calculate the probability of a continuous random variable with a uniform probability distribution

Answer 7

By multiplying the probability density function with the interval

Question 8

What is the normal distribution

Answer 8

It is symmetric and bell shaped around the mean and also asymptotic as it approaches zero for infinity on its edges

Question 9

How can the standard deviation change

Answer 9

With higher variance it becomes wider and higher mean it becomes higher

Question 10

What is the mean and standard deviation in the standard normal distribution

Answer 10

Mean is 0 and variance is 1

Question 11

How can you approximate the binomial distribution when the number of trials gets large

Answer 11

When large it roughly follows the normal distribution where mean is the probability times the number of trials and standard deviation is the square root of the probability of failure times the number of trials

Question 12

Which discrete probability distribution is exponential distribution related too

Answer 12

It is poisson but continuous

Question 13

Is exponential and log normal distribution symetric

Answer 13

No

Question 14

What foes lambda stand for in the exponential probability distribution

Answer 14

The rate parameter which is the inverse of the mean

Question 15

What is meant by the exponential distribution being memoryless

Answer 15

That a happening is not dependent on previous happenings

Question 16

How os the log normal distribution related to tue normal distribution

Answer 16

It is the distribution for a random variable whose natural logarithm is normally distributed

Question 17

In what situations are the distribution log notmal

Answer 17

When values are positive and positively skewed such as income distribution where normal wages are low-ish but the mean is not as low as possible but outliers are very comparatively rich

Question 18

How do you calculate the likelihood of a log normal variable being within an interval

Answer 18

You convert it to a normal variable by loging it and than look up the z score in a table