Question

the conditional distribution of x given x+y is

Answer 1

Answer:

ʜᴇʀᴇ ɪs ʏᴏᴜʀ ᴀɴsᴡᴇʀ ⬇️

Step-by-step explanation:

ɪɴ ɢᴇɴᴇʀᴀʟ, ᴛʜᴇ ᴄᴏɴᴅɪᴛɪᴏɴᴀʟ ᴅɪsᴛʀɪʙᴜᴛɪᴏɴ ᴏғ x ɢɪᴠᴇɴ ʏ ᴅᴏᴇs ɴᴏᴛ ᴇǫᴜᴀʟ ᴛʜᴇ ᴄᴏɴᴅɪᴛɪᴏɴᴀʟ ᴅɪsᴛʀɪʙᴜᴛɪᴏɴ ᴏғ ʏ ɢɪᴠᴇɴ x, ɪ.ᴇ., ᴘx|ʏ(x|ʏ)≠ᴘʏ|x(ʏ|x). ɪɴ ᴏᴛʜᴇʀ ᴡᴏʀᴅs, ɪғ x ᴀɴᴅ ʏ ᴀʀᴇ ɪɴᴅᴇᴘᴇɴᴅᴇɴᴛ, ᴛʜᴇɴ ᴋɴᴏᴡɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴏɴᴇ ʀᴀɴᴅᴏᴍ ᴠᴀʀɪᴀʙʟᴇ ᴅᴏᴇs ɴᴏᴛ ᴀғғᴇᴄᴛ ᴛʜᴇ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ᴏғ ᴛʜᴇ ᴏᴛʜᴇʀ ᴏɴᴇ.

Answer 2

Answer:

In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). In other words, if X and Y are independent, then knowing the value of one random variable does not affect the probability of the other one.