math-eight

Friday, 29 December 2023

Unit 11 - Confidence intervals (Statistics)

1: Expected value with empirical probabilities

1.1:







1.2:










1.3:




Answer: 







1.4:







2: Conditions for a confidence interval (z interval) for a proportion

2.1:




2.2:




2.3:




2.4:




3: Finding the critical value z for a desired confidence level

3.1:
















3.2:










3.3:















3.4:

Saturday, 23 December 2023

y = (norm(x))^2. What is the derivative of y wrt x?

y = (norm(x))^2. What is the derivative of y wrt x?

x is a vector and y = euclidean_norm(x). What is the derivative of y wrt x?

Question: x is a vector and y = euclidean_norm(x). What is the derivative of y wrt x?

Ans: What is euclidean_norm


Ans: What is the derivative of 'euclidean_norm of a vector'

y = w.x Where w and x are vectors. What is the derivative of y wrt w?

y = w.x Where w and x are vectors. What is the derivative of y wrt w?

Derivatives of Hyperbolic Functions

Derivative of sinh(x)





Note: sinh'(x) = cosh(x)

Derivative of cosh(x)





Note: cosh'(x) = sinh(x)

Derivative of tanh(x)

An alternative to the logistic sigmoid is the hyperbolic tangent, or tanh function (Figure 1, green curves):

Friday, 15 December 2023

Alphabets and Cartoons to Color

A for Apple
Apple मतलब सेब




B for Ball
Ball मतलब गेंद




C for Cat
Cat मतलब बिल्ली




D for Dog
Dog मतलब कुत्ता




E for Elephant
Elephant मतलब हाथी




F for Fish
Fish मतलब मछली




G for Goat
Goat मतलब बकरी




H for Hen
Hen मतलब मुर्गी




I for Ice-cream
Ice-cream मतलब आइसक्रीम




J for Jug
Jug मतलब सुराही




K for Kite
Kite मतलब पतंग




L for Lion
Lion मतलब शेर




M for Monkey
Monkey मतलब बंदर




N for Nest
Nest मतलब घोंसला




O for Owl
Owl मतलब उल्लू




P for Parrot
Parrot मतलब तोता




Q for Queen
Queen मतलब रानी




R for Rabbit
Rabbit मतलब खरगोश




S for Sun 
Sun मतलब सूर्य




T for Tiger
Tiger मतलब बाघ




U for Umbrella
Umbrella मतलब छाता




V for Vegetable
Vegetable मतलब सब्जी




W for Water
Water मतलब पानी




X for X-mas Tree
X-mas Tree मतलब क्रिसमस ट्री




Y for Yellow
Yellow मतलब पीला




Z for Zip
Zip मतलब ज़िप