Basics of Probability and Statistics Week 1 Challenge

1. There is a difference in the formula of variance for population and sample because σ² = (Xi - mean)^2/N => Population Variance s² = (Xi -mean)^2/(N-1) => Sample variance The difference in denominator of the sample variance occurs because in a sample, the first n-1 values are independent of each…

AIM :  Data visualizer (100 points) Your script should take column numbers as the input and plot the respective columns as separate images Each file should be saved by the name of the column The plot labels should be extracted from the file. If, I request for a plot between column 1 (crank angle) and column 8(volume),…

AIM : To write code to fit a linear and cubic polynomial for the Cp data given and to find answers for the following questions :- 1. What does popt and pcov mean? 2. What does np.array(temperature) do? 3. What does the * in *popt mean? 4. What needs to be done in order to make the curve fit perfect?   THEORY…

 AIM : To write a program that solves the given ODE, i.e the equation of motion of a simple pendulum with damping, and also to simulate the motion of a pendulum. THEORY :  Shown above is the second order ODE of the motion of a simple pendulum where, theta = angle the pendulum makes with the vertical at any…

AIM : To write a program that solves and plots an Otto cycle, to obtain its PV Diagram and Thermal efficiency. THEORY :  By using the below formula, the plot is obtained (V/V_c)=1+ 1/2 (cr-1)[R+1-cos(theta)-(R^2-sin^2(theta)^1/2)] Thermal Efficiency=1-1/(cr^(gamma-1)) where, cr = is compression ratio And in above…