Suppose the joint pdf of 𝑿 and 𝒀 is

𝒇(𝒙) = { 𝒌𝒙𝒚 𝒙≥𝟎, 𝒚≥𝟎, 𝟐𝟎 ≤ 𝒙+𝒚≤ 𝟑𝟎,,

𝟎 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔

1- Are 𝑿 and 𝒀 independent

2- 𝑷(𝑿+𝒀≤𝟐𝟓)=

3- 𝑬(𝑿+𝒀)=

4- 𝑽(𝑿+𝒀)=

5- 𝑪𝒐𝒗(𝑿,𝒀)=

6- 𝑪𝒐𝒓𝒓(𝑿, 𝒀) =

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# statistics – STAT: Suppose the joint pdf of 𝑿 and 𝒀 is

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Suppose the joint pdf of 𝑿 and 𝒀 is

𝒇(𝒙) = { 𝒌𝒙𝒚 𝒙≥𝟎, 𝒚≥𝟎, 𝟐𝟎 ≤ 𝒙+𝒚≤ 𝟑𝟎,,

𝟎 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔

1- Are 𝑿 and 𝒀 independent

2- 𝑷(𝑿+𝒀≤𝟐𝟓)=

3- 𝑬(𝑿+𝒀)=

4- 𝑽(𝑿+𝒀)=

5- 𝑪𝒐𝒗(𝑿,𝒀)=

6- 𝑪𝒐𝒓𝒓(𝑿, 𝒀) =

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