Let the joint p.m.f. of X and Y be defined by 3x + y 45 f(x, y) = x = 1,2,3 y = 1,2 a) Find fx(r), the marginal p.m.f. of X, and fy(y), the marginal p.m.f. of Y. b) Are X and Y independent? Please explain your reasoning. c) Find P(X + Y <4).

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**Exercise on Joint Probability Mass Function**

Let the joint probability mass function (p.m.f.) of random variables \(X\) and \(Y\) be defined by:

\[ 
f(x, y) = \frac{3x + y}{45}, \quad x = 1, 2, 3 \quad y = 1, 2 
\]

**Questions:**

a) Find \( f_X(x) \), the marginal p.m.f. of \( X \), and \( f_Y(y) \), the marginal p.m.f. of \( Y \).

b) Are \( X \) and \( Y \) independent? Please explain your reasoning.

c) Find \( P(X + Y < 4) \).

**Note:** There are no graphs or diagrams included in this text.
Transcribed Image Text:**Exercise on Joint Probability Mass Function** Let the joint probability mass function (p.m.f.) of random variables \(X\) and \(Y\) be defined by: \[ f(x, y) = \frac{3x + y}{45}, \quad x = 1, 2, 3 \quad y = 1, 2 \] **Questions:** a) Find \( f_X(x) \), the marginal p.m.f. of \( X \), and \( f_Y(y) \), the marginal p.m.f. of \( Y \). b) Are \( X \) and \( Y \) independent? Please explain your reasoning. c) Find \( P(X + Y < 4) \). **Note:** There are no graphs or diagrams included in this text.
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