Basics of ML & AL Week 2 Challenge

2) Expected value: It is the Probability of an event multiplied by the amount of time the event happens.

A Probability Function defines the relative frequency outcomes of a random variable - the expected value.

In case of infinite number of Observations, it is very difficult to note each and every outcome. In such cases the probability of each outcome is determined using this probability. The formula is :

μ=∑x⋅P(x)μ=∑x⋅P(x)

Simple Mean : In case of Finite number of Observations the sample mean is calculated by (Sum of all observations/number of observations) .

3)Having skewness in the curve considered to be bad in the analysis?

A)Skeness: It is a measure of asymmetry of the probability density function of a real-valued andom variable about its mean.

There are two types of Skewness:

1) Positive or Right Skewness: When the tail on the right side of the distribution is longer or fatter. The mean and median will be greater than mode.

2) Negative or Left Skewnwss: When the tail on the left side of the distribution is longer or fatter.The mean and median will be less than than mode.

i) If the skewness is between -0.5 and 0.5, the data are fairly symmetrical.

ii) If the skewness is between -1 and – 0.5 or between 0.5 and 1, the data are moderately skewed.

iii) If the skewness is less than -1 or greater than 1, the data are highly skewed.

Having skewness in the curve is not considered to be bad in the analysis, Skewness is the attribute to describe the distribution.

4)Evaluate the probabilities for continuous normal distribution with given mean = 680 and standard deviation = 31

a)P(X<711)

b)P(X>740)

c)P(600<X<720)

d)P(X=720)

A) Given data : mean(μμ) = 680, standard deviation (σσ) = 31

a)P(X<711) = P(680 + 31)

= P(μ+1σμ+1σ)

In normal distribution the area under the curve which has the probability of outcomes is 0.5

The area under the curve from origin to 1σ1σ is 0.34

Then P(X<711) = P(μ+1σμ+1σ)

= 0.5 + 0.34

= 0.84

b)P(X>740)

We know that

Z=X−μσZ=X-μσ

Z = 740−68031740-68031

= 1.935

By using Z table : P(Z<1.35) = 0.9744

Then P(X > 740) = 1 - P(X<740)

= 1 - 0.9744

= 0.0256

c)P(600<X<720)

For 600:

Z = 600−68031600-68031

= -2.58

For 720:

Z = 720−68031720-68031

= 1.29

Then we can write : P(-2.58 < Z < 1.29)

By using Z table : P(Z < -2.58) = 0.00494

P(Z < 1.29) = 0.9015

P(-2.58 < Z < 1.29) = P(Z < 1.29) - P(Z < -2.58)

= 0.9015 - 0.00494

= 0.89656

d)P(X=720)

Z = 720−68031720-68031

Z = 1.29

The Probability of X = 720 is equal to the area under X = 720 which is very small. we need to subtract area on the left as well as the right side of the curve from the total area.

Therefore P(X = 720) = 0

5)Explain the curve on the right side

A)

For the diagram shown above is the Probability distribution curve for the Normal Distribution.

The total data is centered into 50 % above mean and 50 % below mean.

We consider the standard deviation of the data is σσ then,

68.2% (34.1 + 34.1) of the data will lie between (μ−1σ)(μ-1σ) to (μ+1σ)(μ+1σ)

95.4% (47.7 + 47.7) of the data will lie between (μ−2σ)(μ-2σ) to (μ+2σ)(μ+2σ)

99.7% (49.85 + 49.85) of the data will lie between (μ−3σ)(μ-3σ) to (μ+3σ)(μ+3σ).