A particle starts at (0, 0) and moves in one-unit independent steps with equal probabilities of 1/4 in each of the four directions: north, south, east, and west. Let S equal the east-west position and T the north-south position after n steps. (a) Define the joint pmf of S and Twith n 3. On a two-dimensional graph, give the probabilities of the joint pmf and the marginal pmfs (similar to Figure 4.1-1) (b) What are the marginal distributions of X and Y?

step-by-step explanation:

$11.01

$16

$15

$4

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34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

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