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does Random page replacement algorithm suffers from belady's anomaly?

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Any page replacement policy/algo. suffers from Belady's Anomaly's iff its does not follow "STACK ALGORITHM" . LRU and Optimal always follow the stack algorithm property. So they never suffers from Belady's Anamoly.

You have to understand Stack Algorithm first. 

As far as you question is concerned ,Answer is "YES,Random page replacement algorithm may suffers from Belady's Anomaly".

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i think random replacement can suffer from belady anomaly coz there can be a case when page selected to be replaced is by fifo policy.I think that case might count.
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The main reason for belady anomaly is the stack property. Means the pages when frames were less should be a subset of pages when pages are more. On increasing page frames the page which were earlier there should always be there. If we randomly remove any element then it may be case that we inocuur palenty for pages that were earlier there but now after increasing page fault they may be removed.

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