****** This question is Python lab programming*********

Your initial data comes in the form of counts. These are from the ANES data, and represent ideology (rows) and votechoice (columns).

data = np.atleast_2d( [

[106.0, 4.0],

[366.0, 7.0],

[216.0, 30.0],

[309.0, 205.0],

[85.0, 215.0],

[26.0, 475.0],

[8.0, 123.0]

] )

print(data.shape)

print(data)

1. Write a function that converts a 2D array of counts to a probability distribution.

def counts_to_probabilities( cnts ):

pass

probs = counts_to_probabilities( data )

# the probability of row 2 [0-based indexing], column 0 should be 0.0993

2. Write two functions: one that calculates the marginal distribution of the rows, and one that calculates the marginal distribution of the columns.

def marginalize_out_rows( probs ):

pass

def marginalize_out_cols( probs ):

pass

row_marg = marginalize_out_rows( probs )

print(row_marg.shape) # should be 2x1, or (2,)

print(row_marg[0]) # 0.513

col_marg = marginalize_out_cols( probs )

print(col_marg.shape) # should be 7x1, or (7,)

print(col_marg[0]) # 0.051

3. Write two functions: one that calculates the conditional distribution of columns, given a specific row; and one that calculates the conditional distribution of rows, given a specific column.

print( condition_on_row( probs, 3)[0] ) # should be 0.601

print( condition_on_col( probs, 0)[3] ) # should be 0.277

4. Write a function that calculates the expectation of a function f, given a probability distribution probs. You may assume that the values of x are integers ranging from 0 to the length of the distribution.

def f1(x):

return np.exp(x)/20 + 17

def f2(x):

return np.cos(5*x)*np.sin(x/3)

print( expectation( condition_on_row(probs,3), f1 ) ) # 8.5421

print( expectation( condition_on_col(probs,1), f2 ) ) # 0.5736

print( expectation( row_marginal(probs), f1 ))

print( expectation( col_marginal(probs), f2 ))

6. In a style similar to f1 and f2 above, write a small identity function.